My ex moved out and got a place with his new gf who I didn't even know he was with, I had a suspicion he was seeing her, unsure if he was living with her as when I tried to bring it up he would avoid the subject, he didn't have the kids over for 3 months, even though they kept asking when they could see his new house as they were excited about going to stay, which I hated him for because he would fob them off with excuse after excuse and I knew the real reason why. When he finally took them over I had to ask the day before if he had someone living there, just went to show he has no respect for me whatsoever. When the kids came back my daughter said we met daddy's friend, she lives in the same house and my son shhhh'd her. I spoke to them about it later and my son seemed to be trying to not tell me something, he is 12, my daughter is 8, I don't know how ex introduced her but doesnt look like he said she was his gf, I told the kids it was ok and explained to them who she was, as like I say my son seemed like he was hiding something and I didn't want him to have that on his shoulders. My ex is such a twat and has to do this whole secretive thing. He struggles just to be honest and make life a little easier. They have since been on a couple of days out neither time my ex let me know if she was going or not, I know she did as he pulled up outside my house to pick them up but was careful not to park the car right outside, as she was obviously there.
I can't stop him seeing his kids and he has had them to stay at his about 3 times now and its not great for me as I have never met this woman and its obviously hard, but its a damn sight better then the situation I was in before trying to separate from this man. I can only hope he is taking good care of them when they are there and I have to trust in this, I try and enjoy the time I have to myself, its getting easier.
The kids do not seem to be affected by this, I think stopping them from going to his would have more of a detrimental affect on them.
In an ideal world he shouldn't have moved in with her straight away, but I've learnt that he will never do the right thing, thats why he is my ex, I tried to separate from him for 3 long years and he only left in the end because this other woman came into the picture, which is how I knew deep down he was in a new relationship he would never of left otherwise, he just kept it a secret as usual. I have to thank her in a way, and I have briefly spoken to her on the phone and she seemed normal, 
it's only been a few months so the children might see things differently or it might have a different affect on them as time goes on, I will just have to deal with things as time goes on, but its down to him to put them first I will never be able to control the stupid things he does apart from stopping him seeing them which I will never do for their sake not his.
No doubt if I get into a new relationship all hell will break lose though 