This will be outing to anyone who knows me but it is what it is.
My DDs dad (my husband at the time) left me for OW when she was a baby but omitted to tell me that he was living with her and they had a baby for over two years. He also barely saw DD during this period. I found out because one of my friends saw them as a family with his parents as well (DDs grandparents) and told me. I mean, I was a bit suspicious because of the way DDs dad never took her to his house or anything like that but I had not pressed the matter as I was busy with work and DD.
So actually, looking back, my main reaction was anger that he had this whole other family and DD had a sister she had never met. I felt that it was not fair to exclude her and she deserved more than that. In the end, I met up with him, his partner (now wife) their DD and my DD in the park for an hour so that DD knew who she was meeting before she went over. DD was two at this point. And when DD was little, I made sure to include her half-sister in parties.
In reality what it meant of course, was that DDs dad was not looking out for DDs interests and barely parented her - she went over maybe once a week or fortnight and hardly stayed over even after that, but she has two half-sisters now she is close enough to and that has benefited her life.
It is really difficult because you do need to separate out what you think and feel for what is in the best interests of DC. I recall my solicitor saying when I was saying about DDs dad never taking her to his house that DD deserved to be properly in his life and to know the whole person and not just trips to the park. And in fact, the whole person had a whole other family which DD was not part of. Your ex has a whole other life which DC are not part of.
So I think two things
The first is to ask your ex why he would like DC to meet his GF now rather than in a few months when they have had time to adjust more to the separation (whilst also being clear that you do not wish to help facilitate this) and what he expects that relationship to look like. I say this because it is important to keep lines of communication open.
The second is that i believe in age appropriate communication. I don’t know what you and your ex have told DC about the split. But if they know he has met someone else, then ask them how they feel about meeting her.
I do think you want a situation where DC are able to voice their views and be heard, not one where you one or both of you sit down and tell them what is happening.
I am saying this two decades down the road now but i recognise that you are still very raw emotionally and that it takes at least a year to stop feeling like that. Time heals, honestly, and your DC will grow up wonderful people, and if a half-sibling comes along, ideally this will enrich their lives. Your ex is a shit with no morals of course but that is not the DC’s fault.