If I were him, or her, or one of the children, I would not think all three meeting up is a good option.
As the new partner, I would hope the kids won't hate me, but would prefer to spend as little time in the same room as possible.
If I were one of the kids, I would feel similarly about the new partner.
If I were him, I'd feel that I couldn't be myself with either her or the children, while they're both in the same room. It would be awkward.
In his position, I would intend to always keep my life with new partner as separate from life with kids as practically possible. The kids and the new partner will never be each other's family, and none of them would want that.
On another issue, I would absolutely describe a new partner as a "friend" to my child. Not to fool them, not because the relationship isn't important, but simply because using a word that brings my sex life into the conversation would be awkward for both. I know I have one, they know I do, we don't need to talk about it.