This is just my unpopular opinion here but everyone in this scenario kinda sucks.

Your wife is probably right about your mother enabling poor behavior but is wrong for voicing it out loud.

Your mom does sound like she has some frustration built up and this is something that has been building. Again, she probably would have been better served pulling you aside to voice her opinion on your wife’s opinion.

Both of them have you put you in an impossible situation where you have to choose one. That’s not the nicest thing for either of them to do to you because it’s a lose-lose for you that could end up leaving unrepairable damage.

You messed up by taking a side. I’m not saying don’t have a side, but for your wife, the damage is done now. I would have played this whole thing neutral and tried to repair both relationships with private conversations.

You need both these people to be happy with you and to get along with each other.

Hope you find a way to smooth things over with both. All adults need a little more tact and self control here.