There are men that will date a woman with kids, just make sure not to introduce your children to this man until you know things are going well enough with him to see a future. Depending on how old the kids are, make a difference, baby/toddler/kid- he should not meet them, if the kid is like 16-17, then it would be easier to talk to your kid about your date; still don't introduce them early on.
I dated a guy when my daughter was 1- it was not good.... she needed the attention she needed- because she is 1. The guy wanted the attention he thought he deserved because we were dating. Separating myself from my daughter for this guy I didn't really feel for, just didnt feel right. Guys who don't have kids in there family, and or aren't around kids that much, don't understand how kids act, whining is normal, acting out is normal (of course in mild amounts) he also shouldn't have any rights to punishing the child.
Never leave your kid alone with a new boyfriend if you already have broken the rule of not meeting until you are serious enough to get married.
Some guys pray on single moms, if your child starts acting out or is scared of being with him. MAKE sure to keep your eyes out, or break things off with him. Your child comes before anything else.