Children are people first, children second.
Like any other person they have a right to love who they wish.
Just because you break up doesn't give you a right to terminate the child's relationship.
They key is to treat each other (adults) with respect and honor, allow the children freedom of contact and to maintain loving relationships with children regardless of how your adult relationships fall out.
I've found this easy to do, other people, well they just can't get off the control horse I guess.
It helps a lot if you learn how to be friends with your exes.
"Love As Thou Wilt"