Ok so everyone is different but I can give my take, I used to be that dude that would never chill with a girl with kids, not sure why to be honest
I started dated this chick that was cool and after 3-4 dates she told me she had a daughter that was 1 years old, no baby daddy drama or anything like that. I was scared as hell but she was mad cool so I stuck around

it wasn't easy cause you can't ignore the fact that if your dating someone (and move in together) their kid especially being that young because a huge responsibility for you as well. My boys used to bust my balls and talk mad shyt, but after a while they got it and they all became cool with the situation
Fast forward 5 years we dated for 5 years, we mutually broke up in feb but are still very good friends i see her 2-3x a week, her daughter (who is now 6) is my nieces best friend (who is 7), they have known each other since 1-2 which is very cool and hard to come by. Her daughter is still mad cool with me, and even her family is cool with me, they trust me picking up her daughter from school more so then her baby's father who is a legit piece of shyt. Her daughter is mad cool with my brothers and they are cool with her. It turned out to be a very good situation and I don't regret it at all, to this day she thanks me for helping her through it at, but in the end, it probably helped me grow up much more then she realizes.
To make a long story short, I got mad respect for single moms now and I actually respect then more then any other random female. It ain't easy doing what they do, yea some are mad shady but I am not talking about them, I am talking about your typical single mom. I

all of them.