Well my mother, the ice queen's response to being told I had broken my arm was to say that I hadn't. So beat that.
I agree with pp that if I thought DD was in any pain I would do my utmost to get there, I would go immediately, I would so want to be with her - if you had been at work or comparable obligation I perhaps would understand, but drinks with friends...? But then everyone has their threshold. If she had cut herself, say, and was with her dad, I would feel happy leaving him to it. Something about a broken bone is quite emotive, but that's not necessarily rational.
I agree with other posters that it sounds as though your DH is expressing his anger and upset at your lack of support for him, using the children as a more legitimate vehicle (I don't mean consciously, but invoking the children is instinctively the highest stakes strategy.)
The no maternal instinct line is a problematic one, it taps into all sorts of unpleasant ideas about what a woman should be, and is fundamentally quite vicious. I'm sitting here thinking that I know that DH, for example, would have been similar to you, he would have been happy knowing that DD was with me and being taken care of if hurt and I readily accepted that. because he was a man? People happily accept a situation in which there is a more present / hands on parent (woman) and less present / hands on parent (man).
Look, you need to get to the root of what your DH is really feeling, because it's surely a lot of anger and resentment, and whether that's because of strange ideas about women or a genuine imbalance in your family / emotional needs being met, or one of a dozen possibilities, you need to know. He needs to start talking in terms of his needs, rather than wielding the relationship between you and your children. The example of you going out when one of your children was full of cold is just blown out of all proportion and suggests something else entirely is going on.