You'll likely find as many different answers to your question as there are potential dating partners, Michelle, but your having children would not stop me or someone like me from asking you out. Getting involved in a more serious relationship would be dependent upon your and my relationship more than anything else, with the children clearly being a priority to assess.
In my case, in fact, I love being a dad and have but one adult daughter, so in a sense it would actually be most likely appealing to me to date a woman with children. Again...depends on the woman foremost.
A few caution lights, though, again just speaking from my own perspective (as it's the only one I have):
If the father is truly 'gone'/checked-out by my own assessment, then I would have to gauge how well the children and I interact as a top priority. I'm a pretty likable guy, but not everyone's cup of tea. No one is.
If the father is merely 'distant' and not some kind of an abomination, then for older children in particular I'd encourage that they take the upper road, reach out, and maintain a healthy relationship with him. It's just better for their sense of belonging and being loved over time, IMHO. Obviously, the particulars would matter a great deal in each case and could override this.
With an 'ex' in the picture, something I've learned from life is the importance of assessing the woman's ability to place me at a higher priority than her 'ex'. While that might seem straightforward, I've recently been in a relationship where even with no small amount of remaining animosity between the woman and her 'ex' at two years post-divorce, the 'ex' clearly had a higher priority than me in terms of "mindshare" for the woman -- very lovely, wonderful person and good Catholic that she is -- when it comes to whom and what she's thinking about...even if it's combat vis-a-vis the 'ex.' Not cool, not loving, and had a way of making me feel 'not good enough' even though it truly wasn't about me, per se.
For a previously married woman, with or without children, the potential for a "rebound" or "transitional" relationship is something I'd personally be keeping foremost in mind to avoid stepping into until I was convinced otherwise. A woman who is still in deep pain from her divorce is most likely not able to make her heart vulnerable again (when it's too soon), and even with her having a good heart will be inclined to see her new man primarily in the light of pain avoidance...i.e., as an emotional air bag of sorts...not as the man of her dreams, as she's still in too much pain.
Last words of wisdom, and a reminder for myself as well: "If a person can not be alone and at peace with themselves, then they CAN NOT pick the right mate." The odds of the right person showing up at the right time versus the in-pain person's impatience are just not good.
Cheers & good luck. Prayer & meditation do help!