Never Meet the Kid(s) Unless...
Unless You're ready to make a real commitment to this woman, the only acceptable scenario where you meet the kid is if the kid is too young to ever remember you; i.e. a baby.
You may be pretty crazy about this girl and the both of you may have fun, but just know that if she ever offers and you accept to meeting the little person who, if they're older than say five, will instantly wonder who you are and why you're hanging out with his or her mother.
A good mother is not going to want to risk confusing her child. Even if she wants you to meet her child, if you don't think you're ready to be her "boyfriend," DO NOT do it. This will only lead her on and make things complicated in the end. The term girls always use for guys who mislead them is ASSHOLE. Nobody wants that.
You Are Not Her First Priority
She's a MOM! Her job is to do right by her child(ren) and see to it that they are not only fed but to also ensure that they don't feel neglected and that their lives are enriched and full of meaningful experiences, that will, ultimately, make them contributing, positive members of society. We don't need any more head cases out there in the world than we already have and you, as a boyfriend, or boy toy, or simply a guy with a crush need to respect that you come second, at best. Kids have to go to school, soccer practice, sleepovers with friends, go to the doctor, etc. Patience is a virtue, young man.
Don't Be Insecure
Since this woman you are seeing has offspring that means that she will occasionally have to and meet up with their father. Understand that that has nothing to do with you and you should never give her any grief about seeing him when she picks up or drops off the kids, or if she sometimes talks on the phone with him about issues regarding their child. If she wanted to be with him, she would be. But, she's seeing you because they, obviously couldn't make it work.
Don't Keep a Full Schedule
Once in a while, she might unexpectedly get a night off. Her mother may offer to watch the children out of the blue, the baby's daddy may have got a wild hair to take the kid to the amusement park and she might just want to take advantage of her night off to spend it with you. Be ready for these nights because she'll likely be a mood to make the most of her limited free-time and will probably be eager to hit the town, and moms who don't have a lot of free-time often don't waste time, if you get my drift.
Some Weekends She Won't Be Available
This ties in with the first paragraph of this post, but if you're dating a woman with a kid, or two, there will be weekends where she is "adulting" and will have no time for play time with you.
So, you'll be left to fill your time with you buddies, or maybe even go see your own mother. Depending on the guy, this scenario could be seen as good, or bad. On one hand, you'll typically have two weekends a month to do whatever you want to do. You will have no one to answer to and no one to make you sleep on the couch when you come home too late.
On the other hand, if you're the type of guy that needs to have that connection with your significant other and can't go more than a day without seeing her, you're going to have a problem. Everyone is different and there are without a doubt guys that would love nothing more than to have a couple weekends a month without their girlfriend around, and, by the same token, there are absolutely guys who eat, sleep and breath to see their "honey."
Treat Her Like a Normal Girlfriend
She's still a woman. She still has feelings and, if you two are remotely committed you need to be texting her or calling her and wishing her a "Good Morning" and/or a "Good Night." She still wants to be pampered and occasionally get flowers at work and be showered with affection and taken out and treated like a lady. Don't think she's ever too busy raising her child to not have a need to feel appreciated and loved.
If you do have a woman that has a child that you're thinking of getting involved with, keep all of these things in mind and be clear to her about your intentions and you'll be just fine.