Where do you draw the line?
AIUI the situation is:
- SiL has four children from his previous marriage
- ExW has remarried and had further DC
- SiL has two further children with DD
- ExW is the RP for the SC who spend weekends with DD/SiL
- DD is a high earner and has chosen to send her DC to private school. (presumably with SIL agreement)
- DD has had job issues and OP stepped in to help with fees out of her savings
- SiL has asked her to pay for his other children as well, despite never having paid for their education himself
- SC DM/partner are both out of work, despite having at least 6DC between them
- SC have extended family network of their own with money who decline to spend it on the SC
Surely the issue here is with the SC RP set up and the example being set and their own moneyed relatives choosing not to spend it in the same way as the OP. I'd put money on their home set up being as much to do with their academic difficulties as the difference between state and private (which is not a magic fix for academic struggles).
Why is it the OP's responsibility to fix this problem rather than the SC own parents, DGPs and relatives? The RP/DH could at least get themselves into work.
Even if the OP had the money for the SGDC - where does it stop? Should she fund their half siblings so that it remains fair in the RP home?
I'd be taking a long hard look at the man who fathered six children by two different partners and expected his PiL to provide for his DC by his ex (also the parent of at least six DC). I would be considering trust options to protect my DGC interests longer term.
In general terms its perfectly possible to treat steps fairly without treating them in the exact same way. As PP said - some parents/DGP would object to too much equivalence, especially if they couldn't compete. Treating them differently when on a day out together would be crass but its not unreasonable to buy things for your own DGC when they have a full set of their own family involved in their lives and it avoids stepping on toes.
Every set up will be a bit different - a SC who has been in both partners lives since infancy and is near as damn it adopted/has little contact with their other parent/family is going to become just one of the regular DGC over time. The OP's set up sounds very different