How do I survive summer?

I agree that you need to upfront with them about finances.
You can be very clear that your budget is very limited, and that the treat is the activity itself. They will get used to the fact that they don't get to spend money in gift shops unless they use their own money, that they don't get to buy snacks at the cinema, and that bringing your own picnic is a treat in itself. You can explain that these places are set up to part people from their money, and show them how it's no coincidence that you have to walk through the gift shop in many places in order to get in or out.
You can tell them that you can go out for pizza/burgers etc more often if they have just the main course, no starter or pudding, and only tap water to drink. Or you can give them the choice. They are old enough to understand how this all works.
They may moan a bit to start with , in which case cancel the next outing. You can show them, without having an argument, that treats are not automatic, and that whilst you will always provide them with what they need, you have no obligation to give them expensive luxuries, and in fact you find it distasteful that they are complaining when they are so much more privileged than most. Actions speak louder than words.

Kids know which adults can't or can't keep control - that's how it is with teachers and that's how it is with parents and all other family members. They'll behave exactly how they are allowed to behave with each different person. If their father doesn't allow them to act up, why do you? Do you feel that you are just not entitled to respect in the same way he is? Or are you somehow trying to "make up" for the fact that you don't have as much money as him? Either way, it's not a good message to be giving them (that women don't have to be listened to, respected or obeyed like men do) and it's clearly making your own life a misery. Stop making a rod for your own back, get stricter and insist on the same standards of behaviour when they're with you that he gets when they're with him. Once they've understood the new rules and know you're not going back to the old dynamic, you'll find things a lot easier.

So the eldest's ADHD only seems to manifest when he isn't being spoilt rotten? Interesting.

My 7yo and ASD 10yo DDs bicker for 80% of the time they are together unless the TV is on (sometimes it even has to be separate shows separate rooms). It's so so tough and I feel for you. I separate them when they start to bicker, sometimes if DD1 gets into the groove of something (drawing etc, there are free webinars and videos), I can do something 1-1 with DD2. And vice versa.

We spend a lot of time at home as they are a nightmare in the car (audio book and Bluetooth headphones helps).

Can you leave the 12yo at home for a couple of hours plugged in and do something with the 9yo?

Could you not talk to them at the start of the holidays and make a plan of things they would like to do? They are old enough to learn how budgeting works, so if you explain there is X amount to spend, challenge them how to best to use it over the holidays.
Make a list of activities and factor in costs for them e.g
A Beach Day has parking or travel costs, the price of an ice cream, picnic £15;
Cinema day has tickets cost, travel costs, food £50
Let the boys help plan their time making best use of their budget. Also make them aware that if they save money in some areas it gives them option to do other things. For example if they don't buy food in the cinema they can keep money in the budget to go swimming another day.

You have my sympathies op. It's a hard job.

Ds and I were discussing this the other day and we have figured out that when we do any activity at all we have to budget to use 80% of our energy for conflict resolution and only 20% for actually doing the task. So when we are planning an activity, we think about how much energy we have, figure out 20% of that, and choose an activity that requires that amount of energy.

So far we have spent much of the holiday on a sunlounger in the garden or doing a little bit of gardening. That's all we are good for (we are already on holiday)

Do your kids do chores now as well? I find it's actually a good way to split them up, get them to share the work, and learn some responsibility. My DC take turns to dry up while I wash up. Whoever is drying up gets to choose the playlist which they love. The other one gets to go an read/watch TV (whatever...most importantly they're out of each other's way!). Same with tidying rooms - chuck a playlist on, keep them away from each other (younger DC prefers if I help them/guide them).

Sounds tricky with dad taking them on expensive days out but mine are coming to understand that they can have fun with the simple things. Youngest loves to come to supermarket with me, both love cycling, they both love animals/nature so will come for a walk, both love crafting, building.

Well, that’s on you as their parent to discipline them for rudeness. If they’re rude, no days out at all. Tell them they can take themselves when they earn their own money.

Sounds like you’ve staved off tantrums by pandering to them for years and this is the result.

Mine are the same age and ditto eldest with ADHD (and ASD). They are at each other's throats 50% of the time and good pals the other 50% (but it can change in the blink of an eye!).

Strategies we've employed:
-Brainstorm ideas at beginning of holiday on what everyone wants to do -expensive days out (usually we'll only do two!), places they want to go whihc are lower cost, places they want to bike/bike, actives they want to do at home.
-Make a plan week by week to put up in the kitchen showing fixed things and the activities planned for that week (really helps ADHDer to know what's coming).
-Split the day up into sections for activities/crafts/TV etc.

-Be realistic - we rarely do full days out - that's not going to be fun for anyone with my boys.

-Plan in one-to-one activities (so plan as well what the other one can do independently).
-Get out everyday. I prefer to do this in the morning.
-Build in quiet time - a film, reading, puzzle book.
-Try to make simple things exciting. If we're having a film afternoon we'll have popcorn (and make popcorn bags to use). We sometimes do a theme day and make use of different toys/activities we already have (e.g. LEGO day - mini-figure photography in the garden, lego challenges, playing/building, watching the lego movie or ninjago; knights day they made cardboard shields and painted their own crests, watched dungeons and dragons, did a treasure hunt through the neighbourhood using simple clues I wrote or photos; beach at home day - set up the garden for the afternoon, eat all our meals outside, go shopping for a bbq, set up paddling pool.
-I remind them before we go out someone where (like a zoo) that I am not buying them anything! They still nag, but they're kids - that's generally what they do!

I've just dragged mine out for a 2 hour walk and have lost my mind with them at least 5 times today (and they've yelled at exam other as well). I really do know how you feel

Are you in good terms with their dad? Can you tell your DCs if they misbehave with you, it will reflect on the threats they get from their dad? Do they know it can't be Christmas everyday, and school holidays and weekends are for learning and reading, not just days out

Give them fewer choices. Be a bit passive with the bad behaviour. Mine were told very early that the "spends" on days out were limited to a couple of quid and when it was gone it was gone. They learnt very early that hook a toy, etc, at theme parks were rip offs.

Also give yourself a pat on the back. They kick off with you because you are a very safe space and one that provides unconditional love.

They are also old enough to share a budget with there is x for holiday spending, therefore this covers y day out and after that we need to look for days that are free and make the best of them.

I'm sorry things are so hard 😞 it does sound difficult.

I think first, at 12 and 9, they are old enough to understand that money isn't infinite and there is only so much of it. I would sit them down, either together or separately and tell them bluntly ' we can afford to do x/y/z, other days we will need to do something free/cheaper. If we go to the beach, we cannot buy X as that costs money'.

Then, if possible, make a list of feasible things they can do with you on your days and make a bit of a plan.

Is there anyone else who could give you a bit of help? Grandparents/aunties and uncles? Don't be afraid to ask!

I would try to get outside as much as possible- let them take a football or something each. It's generally easier outside!

I have 2 with ADHD (9 and 10), and the youngest in particular needs to know what I have planned on an hour by hour basis every. bastard. day. He’s also SO loud. When he’s happy he’s yelling and when he’s unhappy he’s yelling.

I encourage them to have friends over a LOT; we live in a village, so we do have quick and easy access to a group of mates, but I also book in play dates with their friends who live further away and they have lots of sleepovers both here & there. Is that an option?

Plus, I get the sense that you feel a bit like they owe you ‘grateful’ but you never get that from them, and because money is tight it’s amplifying those feelings. My DH has a bit of a tendency to think the DC should be more grateful than they sometimes are - but we’re the grown ups, we choose to spend money on them (or not) and they don’t really owe us gratitude - although I do expect good manners and not obnoxious behaviour. You need to change your attitude a bit so you’re not resentful. If that means spending less money on cinema and trips, do that. No one will die and they’re not deprived if they only go to the movies once every six months!

That sounds very positive. Their Dad isn't doing them any favours imo, he's just teaching them to be spoiled.

No wonder you are feeling so stressed.
The hard line is hard but you need to take it for your own sanity. The beach is the treat. A picnic lunch on the beach is a bonus treat. Ice cream bought from the supermarket when you get home after a nice day.

No to anything else.
If they don't want the nice treats, beach, park, cinema, whatever else you have planned then there aren't alternatives. They will learn to respect boundaries.

Their dad is buying their love, he doesn't have their respect.

12 and 9? Oh God, I was hoping it would get better. Mine are 8 and 4 and I have a similar situation with ND DC1 winding up NT DC2 and then being unable to hack it when DC2 dishes it out in return. No proper advice but you have my full sympathy.

Oh and if you can face it, I would definitely take them to the caravan - brazen it out with your neighbours, a change of scene might help everyone. Most obnoxious child does the washing up?!

You get extra money by earning it. Give them a list of jobs to do , once they are done they can have the extra money. Then tell them its beach or nothing. They will soon change their mind

Do they need a break from each other? Can you arrange they go to their dad's separately half the summer? So it's still 50/50 shared care, but you get 1:1 time with both.

A couple of things.

First, harden your heart to complaints. Kids this age are rarely grateful and delightful all day long. You had a good time swimming, then it was shit later on. Those are separate. Focus on the good time, accept that the bad time is sort of inevitable and be more ‘water off a duck’s back’ about it. They will annoy each other, that’s siblings. It doesn’t mean the whole day was ruined.

Second, stop pandering. Say ‘Fine, no beach if you’re going to try to bargain with me. We’ll stay home and get some chores done instead. You’ll both be helping.’ They’ll figure out how to be a bit more grateful and that blackmail is a shit strategy in the long run.

Mostly you have to stop thinking that what you’re doing is inadequate.

‘I’ll go to the beach if I can have I’ve cream/sweets/credit for an online game’
response should be "lets not bother then - have you got a book you can go and read. or maybe you'd prefer to help with housework/gardening/whatever"

Where do you live @Summersad? Do you receive UC? Loads of places do reduce price if on UC. Have you got meerkat movies? You can pay for a 1 day travel insurance and get it sorted you could do Tuesday or Wednesday cinema day. No one can afford to do something everyday.