AIBU not to pay for my sister’s younger children’s hobbies?

Definitely don't pay!
There's absolutely no need for you to justify it, but as shes chosen to have a 3rd and 4th child and to have a partner around this time, it is very different.
Some people who go on to have more children will have more disposable income and the younger kids get more hobbies/holidays etc., equally some people will have had additional children since living costs increased and will have had to cut back. Parity between children when it comes to hobbies and holidays is appropriate for similar aged children; otherwise, its dependent on their parents' income at the time they are of an age to do things.
Also, given that neither older child continued with either hobby, its unlikely there will be future jealousy. I could perhaps understand your sister's concern about fairness (though not her requirement for you to fund it!) if one of her older kids was now an Olympic dressage rider or something, but they're not...

I will also add, I think your Mother has got a bloody cheek. How dare she tell you what to do with your money.

Absolutely not. So cheeky to even think you might/should. Say no. Stand firm.

Oof those are expensive, potentially open ended hobbies! If it had been something like swimming lessons I'd have probably paid it myself, but as I understand it horse riding in particular can really spiral.

That was a different thread and situation. That was a friend, not a sister.

@SheGood True, she's made her life choices.

ABSOLUTELY NO. NO FREAKIN WAY. Your sister sounds like an entitled cf who expects handouts all the time because other people have more money than she does. This just sets a bad precedent for more requests to follow. Next thing you know, you'll be paying for these kids' schooling. They won't miss out on what they don't know about. DO NOT DO IT.

And nor should you. She chose to have more kids.

It sounds like she wants to punish you for her choices.

Why should she care so much about someone else's kids? If the parents were so concerned about their kids having all these opportunities, they should have thought about it before bringing them into the world.

The situation is very different with the 2 youngest and the prices I imagine are too.

YANBU

Horse riding can easily cost £2000 a year in lessons before you’ve factored in the kit. It’s very cheeky request, unless you happen to be extremely wealthy OP. Unfortunately, everything has become comparatively more expensive in the past few years, so it’s actually more of an ask now than when you paid for her older children. Does she even know how much dance and horse riding cost?

Sounds quite selfish. I would happily pay for my nieces activity (she's a baby) if my db can't afford it. But I suppose the difference is that my db would never ask me because he's not a CF.. so I understand your reluctance to help your sister out just because of that but I don't get the whole "I'm just paying for them if they are there to amuse my children"...

@SheGood my sister was left in a horrible situation by her ex.

That's the difference, the children's father is around this time and it's their responsibility to pay for their children's activities.

The issue though is that even they can potentially add up such as away games for football, would OP's sister be able to take her child? Or would that be something else she demanded OP do or pay for travel costs?

Your mum's an enabling twat. Yes you really can not do it for them.

Why not just offer the dance which is far cheaper than horse riding.

After your update, I think you're absolutely right to say no OP. Horse riding - super expensive and it's constant - clothing, boots etc etc and if they show promise and excel at the sport, what next? You have to buy them a horse share or their own pony?

Dance also, constant costs of outfits, shoes and shows. Your sister and her partner (what does he do to support them and how does he feel at his DP asking for financial support from her family?) need to improve their own standard of living if they want their DCs to experience these things.

I think it matters as well. It's entitled to ask for anything but to ask for an expensive hobby is worse. If it had been swimming/football the OP might have been able to offer it for their birthdays/christmas.

I think she's being a CF. Out of interest - when she asked, was she at least very humble and appreciative that this is big/cheeky ask? Or did she come across entitled, like it's a no-brainer that you should pay?

I feel for you. I have a couple of people in my family who have been on lower incomes for various reasons, and it's meant I've always picked up the tab on lots of things or spoilt them on their birthdays and Christmas, whilst not expecting even a card in return. I feel like even though their circumstances have now improved, they still have the expectation of "well she's loaded; she can afford it" (I'm absolutely not btw!) and they expect the gravy train to continue.

Well if you don't want to pay then don't. Just tell your DSis No and have done with it Op.

You’re absolutely right not to pay , I think your husband is being supportive to you by saying he doesn’t mind either way but your Mum is being unreasonable.
Honestly, what a shame you’re having this dilemma after being such a generous and decent soul, you don’t deserve be to be taken advantage of. Hold out!

Your sister should be grateful you've been so generous to her older dc. Rather than demanding you paying for the younger ones!
Entitlement ruins all good things.