To be struggling on 3k per month?

you need a TV license even if you have Sky if you watch BBC channels or iplayer on it!!
Check your Sky package and remove anything extra that you don't use. Also check if you're out of your initial contract period as it's usually cheaper to enter a new contract period with a lower rate. Or drop your broadband speed if you're paying more for a superfast rate you don't need.

They're wrong. That's unlikely. Most couples in FT work would earn at very least £26k on NMW so that would be a combined income of £52k

Is it 3k before or after tax, OP? If before tax, that is very tight.
Does that £60 on phone cover your and DC's phones - can you reduce that bill at all, and put them on very basic contracts? And shop around for yourself.

Can you call SKY and tell them CoL means you have to cancel and keep telling them this until they reduce the charge to you? Or really cancel it and rely on Amazon Prime and Netflix for a while.

Get one

Download 3 months bank statements and put every expense into a category and also have “need” “want” and do a budget. You need to invest the time to get the reward.

£70 a week on petrol is huge!
You also don't include anything like car service / MOT, car tax, buildings & contents insurance, cat insurance / vets bills, TV licence and any personal insurance policies.
Your mobile bill is high unless that includes phones for kids as well and Sky is expensive at £70 (mine is £46!).
I don't think it's a huge amount for 1 adult and 2 children. I earn similar but my outgoings are lower and I don't have 2 kids!

1. Don't listen to your parents unless they are offering some kind of practical support (I don't mean handouts, just advice and support) and ignore their criticism. Perhaps though they are losing patience with you if you are complaining about having no money to them and they see you being frivolous?
2. Sort out your spending. Use the notes app in your phone and make a note of everything you intend to spend before you spent it. It may stop you making impulse purchases.
3. Check your bank statements and see where your money has gone over the last 3 months. How much of your spend was non essential - cafes, meals out, takeaways, clothes you didn't need, nail appointments etc. See where you can stop spending.
4. Get some cheaper deals. I recently switched to Octopus energy and am saving £35 a month. They are also so much better than previous provider British Gas as they don't assume you understand the finer details of tariffs etc! They keep it all user friendly.

It will probably be difficult for you to do all of this and emotionally challenging. But, that will be temporary as you will be able to sort your finances and reap the benefits within a couple of months. If you choose to do nothing then this will not change and you will be in this situation for the long term and, it will probably get worse.

You need to look at bank statements for the last few months and list all the payments and card payments that aren’t what you listed. You need to see where all that money is going. It’s very easy to spend when you aren’t budgeting and watching where it goes.

You then need to budget and plan. It’s boring but it works

Surely even a couple on NMW would bring in more and that’s without taking into account you have children to support as well.

I don’t think many families would cope well on just £3k per month these days, not if you have a mortgage etc.

£600 a month for food for 1 adult and 2 kids?! how much are you all eating! That's ridiculous

Get a meter - £150 is loads for water.

You can cancel sky, reduce your phone bill but even after all of the above you still have 800 a month approx so you must be wasting money left/right & centre.

Get a water meter-£150 pm is shocking. I take it it’s based on rateable value. You will save a fortune. Get quotes for your car insurance. £60 is also a lot for your phone-and tv packages should be cheaper than that. It wouldn’t surprise me if you were on ‘legacy’ rates-ie you just carried on paying after your contract ended. It would help if you put the money saved into savings and had a weekly strict budget for the rest.

Can already think of a few bits you’ve maybe missed like car tax, any breakdown cover you may have etc- sky looks high, I’m assuming you have internet bundled in so you could maybe swap to standalone internet and get something like Netflix instead which would likely be cheaper? However I think by the sounds of it there’s probably either more payments that are small but add up that you’ve not mentioned (for me that ends up being different streaming services, Xbox Game Pass type stuff) or you spend the ‘leftover’ money carelessly.

Also, holy shit your water bill! I live in a terrace and we have baths/showers daily and is only £40pm for us?!

I totally get it, life is kind of shit for a lot of people at the minute because everything costs a bomb and I hate it when people say ‘oh well don’t buy a coffee before work!’ type stuff because everyone needs little things to cheer them up and feel like they’re not working to barely scrape by, but that’s kind of what helped me when money was particularly tight last year. Little unnecessary expenses, getting lunch at work costing £5 a day when I could have packed one, a gym membership no one ever used, it all adds up.

You really could do with going on your online bank back to your last payday, taking out all your necessary bills and then seeing where the rest of the money went. It can feel kind of embarrassing or upsetting if things have added up and you didn’t notice, but it’s really the only way to know what changes you need to make. No real point cutting back on a £3 coffee twice a week if you’ve spent £100 on ‘top-up shops’ without realising or £40 on a load of subscriptions you forgot you had etc.

You've also not included loads of costs in your breakdown:

Clothes
Kids extracurricular costs
Childcare?
Haircuts/optician/dentist/prescriptions
Birthday and Christmas gifts

You need to get a better idea of your true costs. I suspect you spend like you've got hundreds a month spare because looking at your breakdown you'd think you would have but it's because you haven't included everything.

Check out your bank and c card statements to see where the rest of it is going.

I started doing a zero based budget. So every penny is accounted for. You’ve got approx £700 a month left over, so you need to find a home for all that money. Either by creating a standing order so you’re paying yourself in to a savings account, or creating envelopes / pots.
Also cat food is fairly expensive, we spend £15 every month for two cats.
Phone bill, I would look if you can reduce this.
Water is very high, but I think this is are dependent.

150 per week on food is quite high for 1 adult and 2 kids especially as you already separated out cat food from that.
My family spend 120 per week on food and that's with occasional alcohol, treats, etc and for a family of 4 (and there's a teen boy in there!).

You are overspending on some things and have no idea where a portion of the money is going.

That's your answer.

Ignore your parents that's really not a lot to live on, kids are expensive and you have two. Do you receive anything from ex? See if you can get a cheaper phone and energy bill. Use MSE or AI to work out if you could cut costs there. Can you cancel sky and replace with netflix/prime? Set a budget for each child for Christmas and don't go over it. Ask family to buy specific useful gifts like a term of kid's activity, school shoes, pj's.

Paying insurance monthly incurs high interest, you’d be better off getting a credit card with 0% on purchases & paying with that. Then set up a direct debit to pay 1/12 each month.
log into internet banking & download a month into excel and sort it by retailer yo see what you're spending where.

Do you have other smaller outgoings?
Life insurance, contents/building insurance, car maintenance, clothes and uniforms, any subscriptions like Amazon Prime? What about your kids, do they do extra curricular activities that cost? Or money for snacks/sweets when out? What about school lunches?
Is petrol really only £70 or is that just the minimum to get to work and you actually spend more on the weekends?
There's no food on your costings, how much is that realistically costing you?
My household is a large family and it is food where most of our excess spend is!

Your water bill is extortionate unless that includes debt. We have a huge family, not frugal with it and our water is half of that, in a fairly expensive area.

OP you need to go back through your bank statements for a year to get a true account of your spending as it's obvious there's a lot left off. Then get a notebook and write down every expense for a month, coffee, lunch etc. then it will become clear. There's also massive savings to be made in your bills as has already been said. Cut your water bill, cancel Sky, etc. You need to count your pennies and budget.

We were absolutely pissing our money away on nothing last year so we opened a Revolut account and specifically put £100 a month in there for frivolous spends now. Stuff like coffee etc. It’s so much easier when you can see it.

Do you get any beauty treatments? Nails/brows/hair/lashes? I get these done every month and found I never counted them in my monthly spends but this is really where all of my spare money goes.

Well, there's your answer then.
Sounds like you do have spare money, you're just throwing it all away on frivolities.

Everything is so expensive, we spend so much on food that often there is not much left at the end of the month. You are not alone OP