you are confusing being a mother with being there. And AGAIN when you give custody to the father, you give custody to him, just because he is remarried or has a girlfriend does not mean they do the taking care of. Men are more than capable of raising a child.
My 16 yo will be moving to her dad's next school year, she is not, nor does she feel she is being abandoned in anyway. It not much different that her leaving for college except she will live in her father's house and not a dorm.