Divorce Support Forums: What I said, what my son repeated...

Here’s my situation…The divorce was final last month…during the year we were separated and going through the divorce, a new girl friend was paraded in and out of my children’s (boys aged 4 & 6) life about every other month. I don’t care whom my ex is screwing around with, but hate how it affects my children. The most recent girlfriend moved in really fast, within 1 month, and has been around for about 5 months now. I've had no real contact with her.
We had school open house last week, and my ex called and said he was on the way; I could the GF in the background. I was chatting with a family member at the school and looking for the ex, the family member asked who I was looking for, I said “the ex” and that I heard the GF in the back ground on the phone, I also said “If he walks in with her, it will be like a slap in my face”.
My six year old now spent all weekend telling the new GF that I hate her and he hates he that that I want to slap her face. I had not said any of this, I don’t even know her.
When my ex dropped the kids off today at my home, the new GF jumped out of the truck and jumped my case for saying that I hate her and that my kids should hate her too. She had the nerve to tell me what I should and shouldn’t say in front of my kids. (At this point I was ready to hit her! But for the sake of my children I never would)
I told her that I had NEVER said any of that, and that the only things that are said in front of the kids is about when daddy is coming to pick them up and which weekends they have to go to daddy’s.
I told her that I don’t care about her and the ex. She pops off that I should care. I told her “why should I care about a situation that I have no control over.” She goes on to talk about the situation between her, her ex and her ex’s new GF. I told her again “I don’t care. According to all the legal console I have talked to unless my children are in physical harm there is really nothing I can do.”
What is the best way to deal with a person, who I really don't know ( I don't even know her name), and how should I approach the situation with my kids. I'm not saying things in front of them, but they seem to be telling how they feel about the GF as if I feel the same way.
Any advice on dealing with this situation would be greatly appreciated?

I happen to know that my ex is still very active on his Match.com account, still on the hunt so to speak, so I really don’t see his current GF lasting that long, but who knows...I guess I should be prepared to deal with this one for at least a little longer.