The only concerns you need addressed when deciding on a woman with kids is her present state of mind and the beliefs & values she lives by. 

The only questions to have answered is the following:

• “Is she the righteous wife that I need, right now as she is?”
• “What level of involvement socially and legally do the father(s) have in her and the kids life presently?

To be successful in your vetting you need to have clear set of standards for your life that you strive to live by.