I think once you hit your mid-30's if you still plan to date there's more than a very good chance any woman you meet of a similar age is likely to have children.
When I was a younger man, I was a single father. So, dating a single mother didn´t seem out of reasonability. But dates may fail for other reasons as they did.
Time later, when I´m older and released, not from fatherhood but yes from inmediate care of kids, now it´s different but the same. Most of ladies of my generation had been mothers and not a few are also grandmothers. And I would not date one of them if she is not single. So, dating a single mother don´t seem out of reasonability.
When I was dating I always asked for a "family" date (usually the second or third date) for bowling or Play&Pizza with the kids included. I felt it was useless to become invested without checking the (my) compatibility with the kid(s).
Once or twice I recall not asking for another date based solely on the child's behavior/attitude towards his/her mother.
