One of my best friends is poly with kids. She has mostly casual relationships outside her marriage as does her husband. They also have kids.
They don't introduce their kids to other partners but my friend has had a partner who did/does and they seemed perfectly okay about it. More or less like your kids accept their parents having friends.
My friend is also selective about friends socialising with her other partners. So she never randomly brings the boyfriend to a party of a family friend or anything although most people know they are non-monogamous. They didn't want people to "catch" them out on dates.
It works the same as having a social life as being an adult parent. Either the other parent has the child while you go out, or you're both out and they are with grandparents.
My friend has little trouble finding men who are respectful, fun and compatible with her situation. She is reasonable about the fact she is a married woman who is staying married so she is understanding of the fact that these other men won't be centering their lives around her.
Her husband has more trouble finding women who are okay with his limitations over a period of time. He meets women who want to date him often, but then over time, they want more than he can offer and some feel they are entitled to it. He has a girlfriend at the moment though. She is married.
They started out swinging but she found that group too unethical, homophobic and misogynistic in various ways.