A woman who is a single parent managing home and child(ren) in this situation carries a very heavy load. Nevertheless, in most cases in a divorce involving unemancipated children, the mother will get custody unless she is egregiously incompetent.
Although the so called custodial parent of children in the tender years, has become abolished by award children to mothers.
The maternal preference is a complete reversal of nineteenth century practices when children of divorce were routinely awarded to the father who was considered to be their owner.
See Tender Years Preference.