"My mother-in-law refuses to sell us the house."
I'm sorry, but you can't force her to sell the house to you.
"Does he have Squatter's Rights to this property?"
No. I can't imagine that he can argue he's been living there without permission. If he didn't bother entering into an arrangement whereby he was doing more than essentially paying rent/upkeep on the place, that was clearly a mistake.
"There also was a small home equity loan taken out 9 years ago that is still open (father-in-law and mother-in-law gave my husband power of attorney to sign their names.)"
I'm not sure what this has to do with anything.
Husband can confirm with a local real estate attorney. Make sure that if one tells him differently that he make them outline the legal basis for it in a *written* legal opinion; it would be best to avoid paying tens of thousands fighting for something just to line a lawyer's pockets.