This thread has had me gobsmacked.
OP should ask for forgiveness? OP should work extra hours? OP is favouriting her child over her neices and nephews? OP should have discussed it first? OP should compromise and just buy the dc?
It's your money OP, you can do want you want with it, you've done a nice thing, it's often said Xmas is not about receiving, so I don't see why so many posters are suggesting bonkers things like you work extra hours so that your sister can still have your money spent on her.
Do most children assume they'll be getting gifts from aunts etc? Or am I weird that I've taught dd (10) from a young age not to expect anything from others because that's not what Christmas is about and not everyone can afford stuff? So sometimes she gets gifts and is thankful, other times she doesn't and is still thankful because she's getting to spend time with family who love her. My nieces and nephews are the same, there's no expectation for gifts from extended family, just excitement and having time together.
I'm guessing the rest of the family are still doing gifts, sis dc will get plenty, why is a few gifts less making her so angry? A simple explanation to the dc that aunt is giving her money to people who need it more as we have enough already should be more than enough (but I dont t think the expectation of gifts from extended family should be there to start with.) what you've described is absolutey not a snub, nor selfish. Don't feel bad.