I am currently in a relationship with a woman with two kids from an earlier relationship. I have two of my own as well. Things work out well for all of us.
Thing is: when you have children you understand that it's a big step to introduce new people to them. So, if you are dating someone with children, don't meet the kids if you aren't sure that it's going to last. That you love her enough to go through what it takes to be a parent. Because it would be cruel to every party involved if you met them and then bailed out.
Now, to my relationship: yeah, things work really great. Her kids have taken to me quite well, and they seem to like me, and I like them too. I haven't met their father yet, but from my girlfriend's description he seems cool with me and has taken the kids at times so we can get some alone time. They share the kids 50%, they change every week. That's becoming the norm here in Sweden, and if it wasn't for the fact that I live too far away from my kids school, I'd do it like that as well. I take them every friday to monday though, and while it means that me and my girlfriend will have to be flexible in how we see eachother, it's worth it. It's love.
Usually though I stay at her place in the weekdays, because of several reasons: she lives in the city where I work, she lives maybe 2-300 meters from my kids school, and of course, I like it here better than being alone at home. Really, it's come to a point where I use my own home just spend time with my kids, and very little more.
So my tip and opinion to you is: there's nothing wrong with seeing a woman with children. But if you aren't sure about it, don't do it, there's additional work, there will be awkward situations and you will probably need to be very flexible and it will take more work and dedication from you than it would otherwise. If you don't mind her having children, then go for it.
Just know that having children is neither the utopia some family sitcoms will have you believe, nor is it the nightmare that some people will make it out to be. They're just people in smaller size.
I was raised by another man than my father, and it just so happened that I started seeing him as my father, rather than my biological one.