The house is a financial problem; whether you sell it or rent it: It is all numbers.
The mother-in-law is a diff problem.
This all comes down to your relationship, short-term and long-term; do you enjoy here company and love her: It is obviously important to your wife, and it will be for the rest of your life.
In this case, as a back up, if you could not sell it and could derive an income from rent money the mother in law might pay, all while still being able to afford your next home (which you will need to check with a banker on before you do anything) maybe it could work?
That being said, and considering the one caveat that business relationships with relatives can be problematic, renting back the house to her might work better than trying to sell it after three months. Looking at the experience of those who thought that they could make a fortune "flipping" houses, it is easy to see that selling so quickly is not always a good solution.