U have written that in many cases father remarries, but there r other way around cases also. I know personally cases in which there was legal battle for child custody and lady got custody of the child. But after 2 years lady remarried and kid was sent to orphanage. When father came to know about that then he got child custody.
In most of the cases even visitation rights of father is contested and I totally agree with Dr.Dsouza that in most of the cases mother never want visitation rights given to father.