How do you make someone leave the house after divorce papers are filed and they refuse to leave?

Because it is the marital home, no matter how briefly, she needs to file an OSC for temporary orders, including an order for posession of the marital home.  It should be easy to get if the facts are as you state, and there are no countervailing facts you have not mentioned.  Once she has the order for posession the sherriff should enforce it.

If the husband is not violent, threatening or harassing your mother-in-law, it isn't likely to be easy.  Until the divorce is final, the court might not be willing to intervene until and unless something like that, or some other legally sound reason, could be shown.

I wouldn't suggest a "psychological warfare" campaign or anything like that, since it could backfire into a harassment charge against your mother-in-law.  The domestic violence laws are set up so that the victim gets to stay in the house, usually, regardless of which spouse owns it.  This is a situation best orchestrated by an experienced divorce lawyer.