Are we talking about regular old divorce, where the ‘absent’ parent is still involved in the children’s lives, or is this about actual abandonment? If it’s the first situation, I am one of those mothers and have some first hand experience.
My ex and I divorced in a largely amicable way and both of us thought it would be better for our children to live with him, for a variety of reasons. First and foremost, we wanted the divorce to have as minimal a negative impact on them as possible. We lived in a large house, in a great neighborhood. The only house/neighborhood/schools they’d ever known. There was no way I could maintain that house on my own, either physically or financially. If they were going to live there, it had to be with their father. In addition to that, when it comes to day-to-day parenting tasks, he’s just better at it than I am. I’m good at the emotional, developmental, long-term stuff, but I suck at running a household. With three kids, that’s pretty important. We made this decision in the best interests of our children.
I do not feel that I left my children, in any way. While he has primary physical custody (we share joint legal custody), I am very much a part of their lives. For years after our divorce, I still saw my kids every single day. I drove about two hours round trip in order to pick them up every day after school, take them to their father’s house, and stay with them until he got home from work. Doing the usual things… getting them a snack, overseeing homework, talking and hanging out. I basically became a stay-at-home mother who didn’t actually live in the same house as her children.
Now that they’re older (13, 15, & 16), I still see them at least one day every week at their dad’s house, and they stay with me every other weekend, most school breaks and for several weeks in the summer. Since I have a flexible schedule, I’m usually the one to take them to the doctor’s and the orthodontist’s and run errands with them. I talk to them on the phone all the time. We’re still very much a family.
I say all of that ^^ because: That’s what it takes to change people’s minds about what kind of a mother “leaves” her children.
TL;DR: In short, absolutely yes. People still tend to think that if a mother doesn’t have her children living with her she’s either A) an unfit parent and has lost her custodial rights or B) a selfish bitch.