To think I can squeeze into a 5 person car with just 2 other people

I don't understand. Your DS and your DF are going to the same place, for the same reason, at the same time, and said you can't go in their car or stay in their flat? And you said "ah, ok?". That's bonkers, who does that? It's playground bullying.
Why would you keep any kind of relationship with people who treat you like that?

We went camping for a week with 3 kids an 8 man tent and all the normal camping stuff in a normal hatchback wtf do you take to not have room when its only 2 of you ?

Yanbu, they both sound absolutely selfish and horrible to treat you this way. Also you have a health condition so they should be offering as well.

Even that is feasible. I have a copy of a film my Dad did in 1966 when my parents used the mini for camping - two adults, toddler, baby, cottage style tent and all the camping equipment driven from Gloucestershire to Argyllshire.

Well personally I’d happily do this for a family member I loved, if I had to choose between family & luggage we’d take less stuff.

Why do your sister and your dad hate you!

Can you fly one way, Op?
And go down the night before. Take the train home.

Your sister doesn't like you.

It's especially galling that they're attending YOUR family event and having a holiday YOU organised! But, honestly, it's best to just roll with it. Don't make a drama out of it, but don't invite your sister to anything else.

Would you be able to break your journey into chunks of manageable driving? Otherwise, it looks like getting a better wheelie case and taking the train or flying.

Have a lovely time with your son!

Ask your sister again insisting that you will only be taking an overnight bag and a handbag and that you will pay for all the fuel. Remind her that it is only one way.

If she declines ask her if she could manage to fit in your overnight bag.

If you can not travel with sister ..

Sort out the trains and ask for assistance. Could you take an extra day getting there and stay an extra night so to make the most of the day you have with son?

They have said the car is full, so I don’t see how you and your luggage could ‘squeeze in’. You mean that you want them to take less stuff than they’ve planned so that you can squeeze in or you think they’re lying and don’t want to give you a lift?

If I go away with my partner, just the two of us, our car is always full as it’s nice to take lots of stuff. When one or more of our children come with us in the same car, we all have to pack much lighter which none of us like. Last time we went away with out children, we took 2 cars, so I think it’s likely there just isn’t room for you to squeeze in without them taking less, which when they’re staying for longer, is unfair on them.

Either your sister or your dad (or both) don't actually want you to be joining them on their holiday. Are you a massive pita to holiday with, or are they not nice people?

Way more to this.

sensing you and your sister rub each other up the wrong way and closely confined is best avoided. If you say no, I imagine she thinks you’re the problem.

it looks like I’m in the minority here but, personally, I think you are being unreasonable! Plans were made, your circumstances have changed and it sounds like you are expecting your sister & dad to now change their plans to accommodate you. Whilst I understand you are suffering with your heath and sympathise with you, that doesn’t automatically trump your other family member’s pre-existing plans or suddenly make you their responsibility. Maybe they have room for you in the car, maybe they don’t but it’s your sister’s car and she has said no, so that should be the end of it. Whether you agree or not, she clearly doesn’t want you to travel with them and shouldn’t have to explain her reasoning. Your comment about the ‘posh’ apartment indicates you may have quite have differing budgets (comes across as perhaps a bit of resentment on your part?). For whatever reason, it would appear you can’t accept your sister’s decision but you seem to be unwilling to discuss this with her yourself, which speaks volumes to me. Invariably in situations like this; there will be a quite different side to this story that is not being disclosed……

Either they are horrible and mean to not give you the lift, so why would you want to be stuck with them in a car? As pp has put, would dsis give you enough comfort breaks?
Or
There's a back story?

Hire a roof top box from Halfords for the luggage. They would even fit it for you.., not sure where in the UK you are from but a quick google showed a load of hire places. One called the journey centre was asking £68 for 7 days hire for a medium box. All the luggage could go in that. They hire the rooftop bars too if you don't have them and will fit it for you.

Plenty of room in the car then. and probably cheaper than a series of train tickets.

Next objection OP's Sister?

I couldn't be bothered with that tbh, but each to their own.

Arthritis in the neck is horrible. I am sorry you are suffering.
I think you are being unrealistic about travelling all that way. Train would be better. You are going to need a lot of stops in the car. What if the pain is excruciating while she is driving. To expect your sister to do this is unfair. If the journey further aggravates your neck you may not be fit to come home.
Is your son keen for you to see him off? I presume he is an adult so he will not want all and sundry there, unless perhaps it is the armed forces? Could you not video call him?

Weather, some are warm but not water proof, some are thin but waterproof for when its wet but warm, some are for folding down in the panniers if we take them. I have different jackets for different outfits if we're out for the day or out for dinner

@Emma6cat that does seem mean, and you are not entitled at all, can't have that much luggage if they are staying in an apartment for a week. How can they be filling a car boot and the back seats, very strange.

Campings different though as you need tents, sleeping bags, equipment.

a week in a nice apartment? One suitcase is enough.

people travel abroad without a car full of of crap so it clearly can be done.

me and boyfriend used to go camping in a jaguar, every space was filled including the huge boot, there was no chance we’d be able to fit an extra person.

I think it’s incredibly selfish of your family. What are they taking, the kitchen sink? Fair enough if they are taking a dog or a bike or something but seriously they don’t have enough room when they’re going to the same place place to see your son!!! Unbelievable!

Do you and your sister get on? I mean on both sides, do you get on with her and does she get on with you?

That is probably the most pertinent question here. It doesn’t sound like you do from the way she is responding to your requests and if you don’t get on I think that is the underlying reason for why she keeps saying no to you.

Or maybe she has her claws in deep and doesn’t want anyone else realise the control she has.

we thought sil was caring for the in laws until we realised she was deliberately keeping us away to hide her abuse.

this is exactly the sort of thing she did. Oh you won’t fit, you’ll have to take your own car. Oh you can’t stay, the room isn’t tidy.

@Emma6cat

No its not really a holiday for them, they too are doing the journey to see my Son off, but granted they are staying a little longer as they dont work so they said they may as well.

Well it’s bizarre that they are both going to same place to see your son off on his travels but they first of all don’t want to share accommodation & now they won’t allow you to travel in the car. Your sister sounds a bit controlling tbh & your Dad can’t be bothered with the drama she will create if you upset her. Regardless of health it seems madness to take 2 cars or take 1 car & pay for a train in addition.