You're conflating poorly advised economic support with love and it doesn't work that way. There is a greater potential for damage to BOTH of you by becoming financially tied under a false premise.
That said, I agreed to stay on the mortgage while my W seeks to refinance. I know she won't be able to until she asks her father to co-sign, and if she doesn't, I'm going to demand that the house go up for sale. Seems cruel, but financial ties can be cruel and leave a lot of bad feelings.
I'd agree with your assessment - you're writing your own death warrant. How will you feel when you find out she's sleeping with her friend and you're financing their place? And he stands to take your place in the life of your child.