Hmm. Yeah, it sounds bonkers to me to give them all the same amount, but there really isn't anything you can do about what the mum gives the DSCs, and it seems illogical to try to 'match' your kids to that!
I think I'd have to say to my kids "sorry, I can't control how DSC's mum handles it at her house during the week, but I'm your mum and here's how we do it in our house." I guess it's really just the same as if she let the DSCs stay up later, or bought them things you won't buy your kids, or get body piercings...there are gonna be two sets of rules, and the kids will just have to live with that, I think.
I guess, too, that you will need a different 'currency' to withold from the DSCs, since the fining system might not be possible.
My DSCs are 14 and 17. They get a ridiculous amount of pocket money - £20 and £25 per week, respectively. It is a lot, I know, especially given that we are truly struggling financially. It is too much, and that removes any incentive for DSD to look for work (she is in school but could and should be working a bit on the weekends and in the summer). It is more than DSS needs, especially, and he usually has a good stash put aside that ends up going on video games. (and yes, we have had them trying to pay one another to do a chore...which never goes well.)
However, it still works out to be less than what was being spent under their old system, where they did not get enough money to pay for their own things, and so disney daddy DH bought everything they wanted, wih disasterous results. In the old system, they also had no responsibilities, and there was no sense of accountability. Plus, if they lost or broke something, they'd just expect DH to replace it.
Now, we pay for their 'necessities' and they pay for the rest - going out with friends, sweets, 'non-essential' clothing and toiletries (some disagreement with DSS over how 'essential' Hollister aftershave is!), gifts for friends and family at holidays, phone credit... They get about half of the pocket money regardless of behaviour, and the other half they get only if they have done their (pretty minimal) chores. It is not perfect, but it is better than the old system.
They go to school with kids that are much better off than we are, and so they have a distorted sense of what 'ought' to be provided for them, and what things are 'necessary'. It is very tough, as they are doing pretty well, but still I think feel very put upon and deprived!