selling the house to bu shares is a no no...Keep the house =, its your bigest investment I guess. Your wife is not for the idea of selling, this may turn out to be major cause of disaray in future...just in case, just in case something goes wrong along the way. Take the family rather than personal view.
Once you are clear that selling is not an option, then you may look at the various options going forward; renting out or living there. From the outset, renting out appears to hold more weight.