I think you're being too quick to dismiss your anger. A kid is sick and throwing up all over the place--yes, that means your husband comes straight home and skips his sex night.
If it had been YOUR sex night for you and your husband, wouldn't you two have had to skip the sex to stay up with the sick kid? Or been so tired/grossed out that you would have ended up not having sex, probably? So how is it fair that he got to do it with your girlfriend while you stayed home with the sick kid?
Plus, I can't imagine being a parent and NOT wanting to come home to help the spouse and comfort the sick kid. I would feel too guilty even to enjoy the sex night.
The good thing here is that your girlfriend sounds really great. She stepped up and seems to be taking a helpful role as a third partner. That's good!
Maybe the two of you (you and the girlfriend) could sit your husband down and tell him that sick kids come first, spouses needing help come second, and his dick comes third--or not at all.
Seriously, it's fine to take time to cool off your anger while not being tired, but it sounds like your husband acted like a jerk. It doesn't sound like a pattern or a severe problem, but it shouldn't happen again.