I read another one of your posts about Lego referring to your DD1 being 4.9? Two month gap so she's still 4! I don’t think either child at that age understands the situation. You already know you're being unreasonable and calling an innocent 4 year old.
“it must still be raw - first Christmas without him etc. And also it will look like happy families from the outside”. I can fully understand this you say he left in March so things are clearly still raw for you, on the flip side it means they have been together at least 9 months? He dropped it into conversation them seeing DD2 for the first time, but he didn't just do it, he told you his intentions, He could have done it without letting you know in advance. Unfortunately you don't have much say on where he goes, what he does or who with, when he's got them unless you think they would be at risk. Circumstances surrounding OW's can be atrocious but you cannot live life like this and keeping them all apart “just in case”. You don't say no to getting married in case you end up a divorcee or no to having children in case you end up separated, like y0rkier0se said you can't predict how things will work out.
“she seems like a sweet girl & DD1 likes her which is the important thing” The feeling must be mutual for both children, she's asking to see your DD after all. You could be seen as being "clueless and selfish" as you say your ex is. You lead us to believe this is about your children, what's best for them, but it appears to be more of a smoke screen. Your real issue appears to be what your ex and Ow do in life. It's non of your concern how they live their lives, I think the sooner you grasp this concept the easier it will be to move on, stop burning your time and emotions on it.
There is no way to justify your original post calling a 4 year old that could say more about you than it does about them. Children are the innocent parties, that includes all of them and god forbid what you could call future ones, you can't predict how things will work out.