Good choice. Honestly, prime earth Batman likely doesn’t have a favorite child, but if he had Helena than Bruce will spoil this one like crazy.
I think Bruce is so caught up in his war on crime that he doesn’t even think about allowances. It is Alfred who doles out the cash and I’m sure his judgement is excellent. That said, I have no idea how the money is divvied up amongst Bruce’s many wards and children.
I do not forget my soldiers like that.