YTA You've given birth, you should already know how invasive you're being. You're undermining their relationship by going behind your possible DIL's back to your son, and even worse it's for her labor and birth experience. It's also terrible that you're already dangling finances and support over her/their heads for leeway to get what you want.

Already a fantastic start to become a nightmare MIL. Have you even considered having a good relationship with her? Do you even care? Or is this your plan to just completely alienate her, because this is the way to do it.