I can chime in here, cuz this is something that I am running into in San Antonio, esp with women around my age (like you mentioned). It's definitely hard to find a woman here that is attractive, around my age, and doesn't have children. Last girl I tried to pick up (a couple days ago) was 29, a surgical tech, not interested in school, hot as hell (HB 9), pretty face, had a baby girl and a boyfriend (I got the sense she was genuine). At the end of the conversation I had pretty much lost all interest in number closing and I left it up in the air lol... not that it would have gone anywhere. I don't want to deal with most of her 'baggage.' And I think that's what they partially look for in a man they are with.
I am seeing a woman with kids. We actually just had sex last weekend for the first time

She had her ovaries removed so she can't have any more which is a plus (I'm sick yes I know). She basically did everything to arrange us being together, asked for my number, comes over, etc. I knew up front she wanted the D eventually.
You are absolutely right about the support issue. I let her deal completely with the kids, and I even was up front with her about the children support/not wanting marriage.. However, it seems like she is trying to forget about that... Some things she says insinuate that she will eventually want me to take care of them or marry her. Not going to happen! I'm going to remind her again soon.
I recently found out that both children are by different men. Of course that only came out after sex. That makes me feel like another notch on her bed post... isn't that kinda ironic...?
Anyway, besides the kids, she has a ToN of other 'baggage'. I've come to realize, we all do - but she is sick with cancer, so in and out of the hospital a lot (she's only 28) then there's the first ex, who she of course makes out to seem like a douche, and then there's the first baby daddy... sheesh.. what a mess... and I don't know anything about the first guy lol, she never mentioned him till after sex. On top of that she seems to feel bad often, but this is understandable as she has advanced cancer.
I guess the biggest thing to me is as long as you don't get too involved, and don't have to deal with the issues she has, it's not that bad. I have no interest in meeting either of those two guys, and I have been around the children but don't get involved with them too much (go out with them). She seems to understand the relationship is between us and no one else, at least for the moment. So if you are on the same page, that's always good of course.
Where are you located btw? I am hoping to find a place where this isn't common... I'm probably dreaming though...
In order to avoid this problem your best option is to get the while they are young and untainted, I guess that would mean around college. Most women, even the unattractive ones, were in serious relationships/getting married circa/post college. I picked up a girl in the Academy a week ago when I was shoe shopping, she was awesome, but after several days of texting she doesn't respond... Next! But it's not like it's all that better because there are problems with young girls as well....