i'm afraid i don't know about the legal side of your question, but what i do know is that even if your partner is forced into a sale, it won't happen in 3 weeks. Even if you defaulted on the mortgage and they started repossession proceedings, you will still be able to bring your baby home. When /if you have to move, most baby accessories are protable, so you will be able to take them with you.
It might be worth pointing out to her that if the house is sold with negative equity there will still be a debt