In the past I've dated several women who had children. (from toddlers to pre-teens). As long as the mother is in charge of her children (ie commands their respect) and there is no drama going on with her ex then there is not much difference.
However I must admit I was dating these women while in my 20s and I was always up front about not looking to get married.
I had no interest in replacing a child's father. One such relationship lasted for 4 years.
Women with children have just as much a right to have a night out, weekend getaway, or date someone as women without children. Her life doesn't end when she gives birth! :-)
It's really up to her as to how she wants to manage her time and also determine what her "true motivation" is for dating a particular guy. It's probably a good idea for her not to introduce her children to every guy she goes out to dinner with. Some women reserve such introductions only after dating a guy for 3 or more months.