If your partner sometimes texts his ex then perhaps he could mention you are all going out at the wk'end. I'm a step parent & my husbands ex has always (been incredibly difficult) kept him informed regarding her partners (3 of them).
Children pick up on a lot more than we (adults) give them credit for. If the children haven't mentioned you, perhaps it's because they feel they shouldn't, if they have & have received a split second on the spot reaction, perhaps they'll feel they shouldn't mention you again, perhaps they've mentioned you & their mum has taken it in her stride & it's no biggy.
In my experience (both personally & professionally) with children in separated families who don't discus the other half of their lives, with the respective parent it boils down to feeling they aren't able to, irrespective to who that is a reflection on; either a parent who's asked/ insinuated that the child doesn't share info with the other parent, or a parent who is not interested in hearing about the other part of their child's life - either or I'd personally prefer a child to feel comfortable in talking to me than not.
Re your children, I do feel age has s lot to do with it, under 7 they're very little & will rely on adults for many different things - re teenager, young adult - I'd think crack on, with a little person, I would want to know who was caring for my children, who supports & helps & ultimately influences them. Not to control the situation, but because as a parent I feel it is my right to know if my children were to be introduced to somebody who may well become a significant part of their life.
I understand that you don't seem to share the majority of the views on here, but maybe switch it round. Why wouldn't your partner sent just one text message? That's all it would need to be.
What's the worst that can happen if you don't tell her (I personally would be crazy if I found out 3rd hand)
& possibly more importantly - what's the worst that can happen if you do tell her - she can't dictate who he spends time with, your not staying overnight with them, so clearly there is some thought going into the impact of their fathers new relationship on them.
Good luck ??