Women with Children
As a man, I think it would be difficult to take a second wife who has children. The easiest situation to deal with, I think, are women who have been widowed. The Bible specifically talks about taking care of widows and orphans. The children who lost their Father will need someone to step in that role as best as they can.
If their father is still alive and in their lives, he will probably have a connection with their mom still. I see both of these as potential issues that could add major stress to family dynamics. If she left him because he was abusive, neglectful, or absent, then he really has no business leading anyone. If she left him for a more arbitrary reason, then perhaps she has some issues that must be resolved.
What do you see as challenges when considering a woman with children, or even one with a past? What are the boundaries or perimeters framed by the Bible to help us understand?