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.
I know this really worries me. Ex has been in city where her step mom lived still until she starts a new job next month and I've had the kids most of the time so hopefully this isn't an issue when she comes back but I'm going to bring it up. I also messed up when ex first started seeing this guy, the kids would not stop talking about him constantly (bimonthly vacations, gifts, etc. I thought they were engaged) and I asked them not talk to me about him to unless there was something wrong; so basically I missed these red flags by telling me not to tell me about what has happening at their mom's. In addition to the vacations, gifts, etc., what ex was telling me fits the narcissist checklist and I told her a few examples of why. Oddly, she asked if I thought she was a narcissist at this time so I can see she is doing some reflection in counseling. I don't think she is one but I know better than to say yes if I did LOL! I did mention it's a spectrum and a lot of the attributes overlap with other things and left it at that.
I couldn't help but think about OM2 from way back while writing this, IDT he was far off in personality. I always wondered if ex was trying to mother her late friend's kids with that relationship but she was also in an abusive one before me. I've really got to keep an eye out for my kiddos.
My son started counseling because he's having trouble at school and as far as I know this guy hasn't come up so hopefully he hasn't been around. I can see it's making a difference and he is excited to go. I recently got a wake up slap not to forget about his ASD, he's getting older and a lot is changing for him so I'm hoping this can make things a little easier.
Also, while talking to ex she told me if I ever wanted to move back to city where she is now she was up for it. Her new job is remote but she will have to travel between here and there frequently. Even though we talked about it and I explained my point about how it didn't work for me it worries me if things slip back to like the good old days.
