I'm a pet owner, pet lover, owner of a couple of certified therapy dogs who are welcome in local hospitals and nursing homes (plus other dogs who are certified K9 Good Citizens), and co-owner of a pet service business.
So, bona fides
out of the way, and with no disrespect intended to the OP or his mother-in-law, I have to get this off my chest: a 4 pound Pomeranian is not
a service animal. It might be a therapy dog that she needs for her emotional well-being. It might be a comfort dog that keeps her happy. But a service
animal performs physical tasks that their human companion can't perform for themselves.
Seeing eye or guide dogs are service animals.
Assistance dogs (they can be any breed, but labs are common) can help a disabled person live alone in a specially modified house (open doors and appliances, fetch phones, etc.), and those are service animals in the context where they're trained.
Fluffy in a purse isn't doing a thing that can't be done by a nurse's aide.
Just for the record, I don't think dogs should be banned from 90%+ of the places they're currently banned, including hospitals and airplanes. When I was stationed in Germany, I was amused to see that Germans often left the kids at home while they went out to dine, but they took the dog with them. (My first week there, I had no idea the couple at the next table had a dog, until they got up to leave and their GSD eyeballed my plate on the way by.)
On the other hand, I witness almost daily people who swear they would faint if they couldn't have Fluffy at arm's length at all times. Those people need emotional therapy, not dog therapy.
But, thank goodness for them, since they contribute handsomely to our household income.