Snake and Tiger, are we not compatible?

To be honest, these two signs are not compatible according to Chinese zodiac. They both are impulsive, suspicious and demanding. Therefore, it's difficult for them to trust each other.

As you said, you wan to make it work for the sake of your children. So I think you both should work together to reserve your differences and cooperate with each other for your children. By the way, you two have been married for years and have your chidren. Your marriage has proved that you both can still work out. So please do not ask whether you can have a harmonious relationship. Instead, you both should do your best to make a harmonious relationship work out.