I suppose this is more asking for opinions on how you feel about partners your ex subsequently goes on to choose and their effect on your dc and how you handle it.
I split with ExDP about 3 months ago. I know that he struggles with being single and in the past has done a lot of online dating resulting in lots and lots of casual hookups with the odd relationship here and there. (We met on OLD ourselves). We have a two year old dc. The split was my decision and he has made it clear since, as recently as a week ago, that he still loves me and wants to get back together. This definitely isn't happening and I have not given him any reason whatsoever to think this. I'm not looking for another relationship myself and can't imagine being ready for at least a year. If and when I do meet someone I will be waiting a long time before they meet dc, and will only introduce them if I think it's going to be a longterm thing.
ExDP on the other hand, despite saying that he wasn't ready to date when we talked about it a week ago (a conversation that he initiated) has, as he's just admitted yesterday, been online dating since our breakup and been seeing someone exclusively for a month. This wouldn't have bothered me except for the dishonesty of him telling me a week ago he wasn't even ready to start thinking about dating! I'm disappointed that he lied as I had felt we had an honest co-parenting relationship and this has made me mistrustful of what he says about anything now.
The other thing that concerns me is what he has told me about this woman he's seeing. I didn't ask for any details but he just sort of blabbered on about her - they've been seeing each other a month. She introduced her three children to him within two days of their first date. Last weekend she told him she loves him. Now to me this does not sound like someone who is in an emotionally healthy place and rather sounds like she is very needy and keen to rush things. And he is not only not very complimentary about her but is saying he's still in love with me, but is intending on carrying on seeing her. The whole thing is completely baffling to me.
I'm aware this 'relationship' if you can even call it that at this stage, may well not last long enough for my dc to be introduced but if it's not her it'll be someone else who, knowing his indiscriminate approach, could very well be quite dysfunctional.
I KNOW his choice of partner is nothing to do with me and there's nothing I can do, and the dc will have to spend time with whatever person he happens to be with at any given time. But I hate the thought of them being exposed to it, and I guess I'm asking how others have handled this issue.
I think the fact that I had terrible experiences with very unkind step-parents when I was growing up is fuelling my anxiety about this. Please don't be too harsh on me - again, I know it's none of my business who he's with, but I don't want my dc to suffer the way that I did.