What is the way to deal with a wife who is quick to anger, who gets angry for the most trivial reasons, and is affected by spontaneous and unintentional actions?

You should continue to be dutiful to your mother without oppressing your wife, and give every rightful person their due. It is the wife's right to have an independent dwelling, and it must be provided for her, even if by renting. Your mother should be advised gently if she is verbally abusive to your wife, or you should delegate someone whose advice she might accept to counsel her.