No, I don't think she should. He's already been overpaying so that's prerogative, but her asking for 2K more after getting 18K is crossing a line and there's no indication that she's going to stop especially because:
This child is 1 years ago. You're bringing up private school that is years down the line. As stat s up thread, private school does not cost 20K a month, and on top of this, you are saying in your own words that private schooling was a need for the parents, not you.
Marlon's daughter will be attending private school whether her mother is getting 20K a month from Marlon or not. This woman is going to be staying at home because, again, this support is already 200K/year in untaxed money. So this lifestyle you're talking about is already accomplished and demonstrating that it's about the mother's wants and not the child.
Unless you can find a private school that this girl will attend in 4 years that'll eat up this monthly support, you need to show me something better than a private school example.