I can imagine what happened is that the eldest is now at secondary school and mum has been shocked at the costs of uniform. She asked dad to help contribute, he said that he was already paying extra and had nothing more to give her because he has bills to pay, and that's when she said that OP could contribute more towards the bill now that she has a better job so he has more disposable income.
Either way, it sounds she is just being greedy. She doesn't have childcare costs, nor housing, got decent maintenance, she is doing very well and should count herself lucky.
Saying that, I'm amazed that some think that kids don't cost much more when they are with the resident parent.£
If we forget the obvious, bills, housing, bigger/reliable car, there is still a lot to pay. If the kids are 12 and 9ish, there will be:
- two mobile phone, likely £40-50
- school dinners: £80-£100
- clothes: £100
- potentially transport to secondary school: anywhere up to £100
- activities AND everything to relativity. Sporting kits, music instruments, petrol to take to events: potentially up to £100
- gifts for birthday invites, pocket money or cash for trips into town, cinema, swimming, bowling etc... especially during holidays
- extra school costs, outfit for xmas show, book days etc..., ingredients for cooking class
- hairdresser, over the counter medicine, potentially teeth retainers
And on and on.... I worked out that my kids with in primary school cost me about £300 each per month and a bit more in secondary when clothes from Tesco didn't wash any longer, mummy cutting hair either, school uniform and activities much more expensive.