Wow! The living situation you describe sounds as far away from God's definition of marriage as you could get. When asked about divorce, Jesus responded with the following. "at the beginning the Creator made them male and female,’ and said, ‘For this reason a man will leave his father and mother and be united to his wife, and the two will become one flesh.' So they are no longer two, but one flesh. Therefore what God has joined together, let no one separate.” I really don't know what to make of it, except that you are quite right; there is a problem somewhere.
You neglect to say whether your"children" are by this husband. That might help to explain the situation if they weren't. However, as a man who has had my share of marital problems over the years, I can assure you that your husband is having an "affair" with something. While it may not be another woman, there is some thing in his life that he values more than you and your children. In my opinion, you can not begin to combat this problem until you know what that something is.
I would suggest that you confront your husband, in a conciliatory and loving manner but confront him nonetheless. Tell him how you feel about the situation and ask what you have to do to create a normal, loving family relationship. And you need to be prepared to really listen to his answer. Whatever, the issue(s), you must be prepared t meet him halfway and work together to resolve them. (This might include finding a mutually agreeable house somewhere where the schools are "good".)
I can tell you from personal experience that divorce is rarely the right answer. God is firmly against it. Jesus said, "But I tell you that anyone who divorces his wife, except for sexual immorality, makes her the victim of adultery, and anyone who marries a divorced woman commits adultery." (Matthew 5:32) However, marriage is a two-way street (if you'll pardon the cliche'), and it sounds like you and your husband aren't even on the same block.
God be with you in your struggles.
