> This policy appears to disincentives children staying with their mother even when it is preferred.

It does no such thing. If you could afford to be a stay-at-home mom before, this isn't going to make any significant difference to that.

Think of whether it would make sense if you applied your logic to other areas -- do public schools disincentivize people sending their kids to private schools? That would be absurd to say. Creating choice where there wasn't any before doesn't "disincentivize" anything. It gives people options to make the choices that are best for them.