Your MIL's main issue is not grief over the loss of her husband. The squalor you described that she tends to live in (animal excrement and accumulated trash) indicates difficulty coping with life and possibly some mental health impairment. It may be that her husband, when he was alive, helped mask her problem of not adequately coping with life by taking care of a lot of things, including her. Now she's on her own, and just keeping up her home is proving to be beyond her. This lady sounds psychologically damaged and, at this point in time, that probably results in behavior patterns that she doesn't even have a lot of control over. She's not going to change.

My point here is that you, if you view your MIL as someone who is not playing with anything near a full deck, can reset your expectations. As a daughter, your wife sort of can't see the forest through the trees, so to speak. She has spent her whole life hoping for her mom to be what a mom should be. She may lack the objectivity to see that her mother lacks the capacity to be anything other than what she is. So they probably have the same pointless verbal exchanges over and over. You're in a position, as a more objective bystander, to see the futility of what goes on between them.

The phrase, "between them," is very important. Some of this stuff you've got to just leave alone as their business . . . and not yours. Sometimes the best thing you can do is to stay out of it. Still, you can't have your wife's time, attention and energies being unfairly consumed by a chaotic relationship with a mother whose life is - and may always be - a mess. Here's where you need to muster up all the finesse and diplomacy you possess. You need to discourage your wife from being over-involved in trying to solve her mother's problems. You need to do this when the two of you are alone together, not in front of your MIL.

As time roles on, the right course of action depends a lot on your MIL's age. If she were 75 y.o., I would say she probably needs to sell that house and go live in an assisted living facility. If she's more like 60 y.o., then that's not going to happen. A lot also depends on how well your wife and her siblings can collaborate with each other in figuring out how they, as her children, can best be supportive of Mom. She's their mother - and not yours - and you kind of have to leave them to it.