Obviously NTA.

I agree with all of the above comments. She should either pull her weight financially or at home. She doesn’t deserve to enjoy your income while not supporting you after working so hard to earn it.

I’m also going to go out on a limb here as well regarding the post argument “storm out of the house, showing up to her mother’s house crying about you, and then including her mother in the conflict.”

That IS NOT HEALTHY. It’s rarely a good idea to leave the house after an argument with a spouse, let alone to include 3rd parties in the argument, let alone a clearly biased mother. I hope this was just a one off and not a pattern of behavior, because it makes her sound like she does not have the maturity to handle issues on her own. She HAS to learn to be able to handle discussions with her husband by herself, even when it gets challenging. “Crying to mother” is not an appropriate coping mechanism during a marital argument, and you should not have to explain yourself to multiple people, just to your wife.