I guess I would just suggest you VERY carefully think through the probable outcomes of his situation. OK, so the kids are in a better school. Will that help that much when their mother implodes? (And from what you are describing, it's not a matter of WHETHER she will implode--what you are seeing right now is the very BEST you can realistically expect). Alcoholism is progressive. It may be hard to imagine how it can get worse, but it inevitably does. Have you talked with a lawyer about how you can protect them when that happens? You might want to look into the law in both jurisdictions to find out where you have the best shot at being allowed custody when your partner gets worse.
I'd just do a lot more thinking and planning before undertaking a move like this with kids involved.