I've been a stay-at-home dad for 8 years and a lot of people have the same view as your mother. I've got a 16 year old from a previous marriage, 8 year old, and a 3 year old.
I have become socially awkward over the last decade because of it. I hate meeting new people because i know that more than likely, I'm going to judged that way. Every so often I'll run into the occasional Neanderthal who thinks being a stay at home dad means I sit on my ass and play video games all day. Far from it. Had more time for gaming when I had a full time job.
Btw, I'm a stay-at-home dad out of necessity, not by choice. My wife is a doctor and makes about 4 times as much money as I did when I left the workplace. We don't have a village to help us raise our kids. No grandparents, aunts, or uncles around that can help pick up and drop off kids where they need to go, help take care of them when they are sick, or watch them in the summers when they are out of school. Its all on me.
Its not easy. I do everything. Run kids everywhere, have a 4000 sq. foot house to take care of, yard mowing, landscaping, all cooking, cleaning, grocery shopping, doctor and dentist appointment running, getting kids on the bus, having to always run one of our 2 dogs and 1 cat to the vet, take care of all vehicle maintenance, i mean this is just the tip of the iceberg. Very few days where I can get an afternoon and not have anything to do. I posted this long list in a similar thread of what I do on a daily basis, and some guy here posted that it was bullshit because the stuff I do is done in every single household, but he failed to realize is that very seldom does all of this stuff completely fall on one person in the household. These kinds of duties are usually split and not fall all on one person.
Its a thankless job, but I don't want to complain too much. I have a good life. Its just very socially isolating, and hard on the male ego. We aren't hard-wired to do this kind of work.