Actually the question isn't gender specific. This question is asked regularly here, by both men and women.
Though I can't help but find the irony that so many people who view themselves as such solid Christian's all coming here and still can't find anyone. Makes me wonder if people should focus more inward and less on their wants.
While I agree about dating women with kids, but not for the reasons you give.
Plenty of married or single parents are selfish, flaky, cheating, etc... the act of having kids does not suddenly improve a person or suggest they're more likely to have better characteristics. That's a false logic. Mumble rap alone is evidence that having kids doesn't make one a good person, parent or spouse
The traits you describe can be just as solidly found in childless singles. A persons character is a better measure than their external circumstances.
For me dating someone with kids has nothing to do with that making them have good character but rather getting to connect with kids and provide a role in their lives that is often either missing totally or is insufficient to their needs.
The reality of dating a single parent is a risk of greater difficulty actually. Kids that may not want a new parent or person telling them what to do. A parent who may put their kids above you (even in marriage) and the like.
So finding those priorities and character are important beforehand. Not assuming they have them already.
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