I'm scared for my kids future relationships. Am I being irrational?

So my ex and I had a horrible marraige with arguments over the most stupid things (usually her twisting my words to mean something completely different) and her being verbally abusive, controlling, and psychologically abusive... That being the case and with most of my other relationships before her being short lived and always initiated by the female, I'm not really the best at starting conversations, being truthful without saying too much or the wrong thing.

My ex has been in 2 relationships since she left me. The first one started as an affair when we were still married and she moved in with him 2 days after I found out. Dragging the kids back and forth between their home they grew up in and the apartment she moved into with the guy... It lasted 3 months. Second started a few months ago after we had the divorce parenting class where they said not to bring people we were seeing/dating around the kids until we were sure this person was going to be a constant in their lives and a good influence (we had both came to an agreement not to have them around when the kids were with us. It was her that brought it up and I agreed for the kids sakes).

So as soon as she started seeing this new guy he was sleeping at her place pretty much every night. Including when the kids are there. I asked her to not have him there when they are and, surprise surprise, it ain't happening.

Tl;dr: I am socially awkward and don't know how to start a normal healthy relationship. My ex is just dropping guys into their lives.

So between their mom doing something both my therapist and the parenting class said not to do and me not knowing how to have a healthy relationship, let alone talk to them about one, am I being paranoid I'm thinking they're not going to have a chance at healthy relationships because of us?

Also, what is the best advice you can give me for when the inevitable happens and I am asked for advice?