Being a public school and your wife signing her up, your daughter has to go to the school within the boundary lines. She didn't do this to aggravate you, I imagine. This is if its a public school. You are saying this before bringing both schools up and looking at their ratings? See how they compare and then complain on how bad it is. It maybe a better school. Your assuming since its by a tin can, its a worse school. Before jumping the gun check it out.
Where I am at, the schools are so crowded that if you are not in school of choice already, you have to go to the school assigned to your area. So first check the school out according to the ratings and then you have some cards to deal with. Also transportation is on you if your not in district.
You have to learn to deal with your wife calmly and in good terms in order to get what you think is best. By getting angry enough not to talk is just telling her to go ahead and do it your own way.