YTA. If you are preventing someone else from contributing because they can't contribute as much as you but will equally share the credit, that is your pride talking and nothing else. Fuck your pride.

Who cares how much they contribute. You said your stepson knows the truth about everyone's financial situation, so you blocking the other woman will just risk creating unnessary resentment. If you do go down that path, I hope your stepson is smart enough to not see your actions as appropriate, since if he does he may start thinking that making himself appear better is more important than other people's happiness (i.e. he will become a pridefull asshole). Is that the example you want to set for him?