In a mother vs. wife fight, you are just lose-lose. ;; Sorry man. Since there's kids involved, I would sit the women down together (since women tend to be more behind-the-back manipulative than in-each-other's-face aggressive, they will probably both act more civil if you make them both sit down with you together to talk) and tell them they are acting like children and for the sake of your kids, you need them to straighten up. Make sure not to take sides, though! I would say your wife is in the wrong because it's rude to try to guilt someone into doing something they can't afford. But your mom didn't react maturely about it, either. But if you act like you agree with either of them over the other one, you'll have a whole new war on your hands.
I'm lucky that way-- my husband and I both think my stepmother is insane, and we both think his mother is strung a WEE bit too tight, lol. So when either of them start acting up, we just ignore them until they chill. Not ignore them, I should say, but ignore the issue.
Example:
On mother's day I called my stepmother. It went to her answering machine because she was probably still in church when I called. I left her a message and said to call me back whenever that day. She never called back. The next morning I had a nasty email in my inbox saying how it was so sad that I was too busy to call her back because she would have loved to talk to me on mother's day. I thought she was being childish and stupid, so I ignored the email. Just like it never happened. I waste a lot of time, but I make a point to try not to waste time on petty drama. When she sent another, more civil email, I responded.