It is a minefield, doesn’t matter what you do, it’ll be wrong to some. You could spend a grand and be told you are overstepping, or spend a small amount and be criticised for having more spare and choosing not to buy them things their parents can’t because they are in benefits.
Do what you feel comfortable with. I don’t agree that you should play no part in the budgeting, your the one who’s responsible for financially providing for the not only the children but also their father, yes, it’s family money, you’re a member of the family and get to play a part in the budgeting, you and their Dad sit down and plan. Every bit of disposable income doesn’t need ringfencing for them, if you can afford £2,000 doesn’t mean it has to be used and you can say £100 each for eg.
Stepmums are often told they should treat the children like their own, should cook for them, clean for them, do their washing, pay for them but where decision making or discipline or fun stuff like watching sports day etc is concerned then they get told they are not the parent, to back off, that they are overstepping, etc etc etc.
You can’t win.
Do what you feel comfortable with, also, the concerns of them taking advantage went through my head too.
Does mum pay child support and Contribute towards her children, who pays the extras like school uniform and school trips? Or does she coincidentally not feel undermined every other day if the year when you’re paying for stuff?