Lama Ole’s answer:
Like in other areas of life, the partners in a marriage want to have happiness and avoid suffering. In this respect, the marriage is no different from any other relationship between a man and woman—with or without the marriage certificate. Both partners are always free to do as they wish. But this changes as soon as children are born because they depend on their parents. When kids are involved, a couple should try to stay together, even though it might be difficult to find a common language at times. In this case, it would be better for the children to sometimes spend more time with the mother and sometimes more time with the father, as the children like.
Our attitude is what matters: we should support the other person’s growth and development, which means giving instead of taking or exploiting. To do this, we basically need to see our partner as something very precious, as somebody who is able to develop.
Lama Ole’s answer:
When taking a human rebirth, a person will be female if the karmic bond is stronger with the father or male if it is stronger with the mother. That basically means that girls feel more drawn to the father and boys to the mother.
This can change throughout one’s life due to other karmas. I believe that the simplest solution is for the children to live with the parent who has found a new partner with a good connection to the children. This is especially true if one parent doesn’t find a new partner. A family is certainly better than a single parent, unless the bond with that parent is particularly strong.
In most cases, I recommend having an extended family, the way the Nepalese live, for example. In their culture, former partners and their new partners create two families out of one, where the children can maintain a good bond with both parents. In this situation, it is important that the former partners do not feel anger towards one another for being left. Both have to be satisfied when they separate.