Leaving your husband for three years for law school in New York while he's in med school in Louisiana will result in divorce. You may say it won't, but I guarantee you that it will be more difficult than you could possibly imagine. I'm in law school and my significant other was in med school 1.5 hours away and there is no way it would have worked for the duration of my three years. Luckily she was able to transfer to a med school in my city after the first year.
Another thing to consider, do you really need a Columbia degree and the massive debt living in New York will bring? Your husband is going to be a doctor and you will be a lawyer, I think the two of you should be able to manage.