She told me about how she found herself in an emotionally and verbally abusive relationship and that she broke up a year ago and he won't leave her alone and showed up.
Oooh, red flags, red flags. I don't now how she can assure you he won't be around the kids, since he could literally show up at any time? Abusive ex's can be extremely dangerous, I'd encourage your exW to take this seriously and file for a restraining order if necessary.