Should I sell house and pay difference of mortgage amount?

The house appraised for 4k less then what we owe so we're looking at paying about 12k for the shortfall and all of our closing fees. We want to move to get our daughter into a better school zone and also the house we have now is very tiny (800square feet) with no garage. The plan is to move in with my mother-in-law who lives alone so we can take our time to buy a new house and save back the money we are about to lose. The issue is we are talking about the house coming in at 96k so that's a big chunk. If I needed 12k to sell a 300k house it'd be easier to swallow I guess. We are one of the one's that bought the house at the wrong time. The goal is to move into a better neighborhood and start life fresh but is that worth 12k? Many people say yes and some say no. It will definitely ruin our savings so we'll need to save at my mother in laws.

Read more: Should I sell house and pay difference of mortgage amount?