To think that parents get to make decisions on their own time

Yes… but both parents should agree to it before they sign up. I doubt the mother would appreciate OP’s partner unilaterally saying “I’ve signed DC up for this, it’s every Saturday, and you have to do it regardless”

If it’s a weekly club at a weekend, parents do both need to make it happen whoever’s weekend it is.

The other parent doesn't get to decide what the kids do when they're with the other parent. I think if there's a club or sports team or something that the kids love doing, then certainly it's reasonable to say 'You'll need to take DS/DD to their football/swimming/gymnastics lesson on Saturday', but no, she shouldn't be deciding what they wear, who picks them up from school, where you take them on a day out, what they have for tea etc. It's up to the parent who has the child at the time to decide those things.

There's another thread at the moment where someone's ex-husband wants to be able to have a say in what house the OP rents and what childminder she chooses. Everyone has correctly told her that being the child's father doesn't mean he gets an equal say in what the child does when he's with her.

Devils in the detail. You can't really sign a child up for a class and then they can't go every other week. Life just doesn't work like that. I've had a lot of issues over the years with my ex not valuing the kids' as independent entities with their own interests and just expecting them to miss things or drop out for his convenience. Ideally these things should be agreed in advance between both parents but it depends on the time split and dynamics. Top priority though should be the childrens' development and hobbies, not point scoring.

He needs to reply to each request with the same phrase until she gives up.

Something short and to the point like, 'I will decide on that'.

What matters is the childen - if they want to do activities and see friends and go to parties it’s unreasonable not to support them

if she needs you to do some of the admin - replace a pair of shoes - well that’s also reasonable

Can you go into more detail?

I think it’s reasonable for mum for expect dad to facilitate swimming lessons and extra curriculars that the dc want to do and are already paid for. It’s also reasonable to expect they are picked up by dad at least some of the time, fed a moderately healthy diet taking into account any dietary requirements, and dressed in clothes that fit them.

It’s not reasonable for the mum to dictate that dad should take them to the most expensive soft play, or that they can never be picked up by yourself or another family member, or are never taken to McDonald’s, or have to wear Gucci clothing.

Is it aftershool clubs that they want to go but you can't facilitate? I don't think there is enough information here to answer.

Unless you're neglecting the DC or putting them in danger then their DM can't legally dictate what happens on their DF time. Is their certain things she doesn't like them to do?