1- As a first step, I recommend you do your best to creatively remove the tension between your mother and wife. Sometimes with some creativity it’s possible to achieve that. Brainstorm, see how tension can be avoided, and gently work on both sides.
2- If that doesn’t work, and you realize no matter what you do the tension is there, then it’s best to move out. Your parents might get upset, but try to compensate by showing them more kindness. Constantly check on them, serve them, be there for them, and show more kindness to them than before. This will help reduce their disappointment.