Just by way of background, we were together 12 years and separated after OW contacted me about their year long affair. This was almost 2 years ago. He was and continues to be EA towards me. I've since moved on and I'm currently in a relationship. I have two issue at the moment.
The first involves our eldest DD(6). She recently told my ex that my BF had dragged her upstairs and smacked her. This is completely untrue. Ex has disliked my BF since we got together and both our DC are well aware of this. DD seems to like BF and they get on well so I can only assume that she has said these things because she knows it's what ex wants to hear.
Ex asked me about the allegations and I was honest and said that she must be lying because I am always with BF and DD so I would know if something like that had happened. He should know me well enough to know I wouldn't stand for anything like that myself but of course it suits him to believe it. Ex is adamant that dd would not lie to him even though she has since retracted the part about the smacking still insisting that BF dragged her upstairs. I've asked her why she has lied but she just says she doesn't know.
I'm worried about what Ex will do now. He loves nothing more than a bit of drama and I suspect would like to see my relationship fail. I'm also upset for BF as he's understandably upset that dd would say these things. What can I do to convince Ex that dd is lying and stop dd from making things up to please her dad? I've already tried to explain to Ex that his openly disliking my BF (even though they've never met) is damaging to our DC but he won't listen and I find it impossible to coparent with him.
The second issue relates to ex's new GF. In all honesty, I was looking forward to him moving on as I naively believed it might take his focus off my life and relationship. My DDs told me that daddy had a girlfriend but said they hadn't met her. When they told me her name, I immediately knew it was the OW. He completely denied the affair at the time and she even messaged me months later saying she had made it up. Because he refused to admit to his affair, I agreed to sign divorce papers based on my own infidelity even though morally I feel I've done nothing wrong as if separated from Ex many months before. Now I know that he is in a relationship with her, I feel angry and manipulated all over again.
She is of course welcome to him good luck to her but having googled her 2 years ago when she first got in touch, I found out some rather unsavoury information about her such as her past drug and alcohol problems as well as her violent criminal record. She also admitted to being on drugs at the time she contacted me when she tried to make out that she'd lied to me. I was always of the opinion that Ex could move on with whomever he wished and that I wouldn't interfere when it came to him introducing our DC but I'm not so sure given what I know about her. WWYD given the situation if anything?
Sorry for the length of this but I'd appreciate any insight anyone has. TIA 
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