You need to do something about this soon, because it is really important for your daughter that you and your husband do not split up.
Your husband is being rude and immature as a response to this situation. Ignoring people for days is childish.
HOWEVER: You cannot take sides with your mother in fights against your husband. That is VERY destructive to your marriage. Three weeks is WAY to long for your mother to stay at your house. Especially if she is the kind of person who "pipes in." If your husband got that mad at her, she is probably somewhat of an irritating person. Remember -- it is your husband's home too, so he shouldn't be subjected to someone for three weeks.
I hope you've worked it out by now, but I suggest you apologize to your husband for yelling at him. Ask him how long he would be comfortable with your mother staying in the future. Make him feel like he matters as much or more than your mother, and then maybe at the end of the conversation, or better yet at some other time, ask him politely to not ignore her when he's mad.
Your husband's own mother obviously never trained him properly about some things, like politeness and etiquette, and that's not his fault. Unfortunately, you will have to take on the task of training him to be polite yourself, but know in advance that it will take YEARS, and you have to do it very delicately. When you criticize men, they will withdraw and become WORSE.