If they tell you something is fine xxx and then get mad about it with other people, then they're being really dumb and pissy about it.
If you give them the silent treatment over the fact that they did that, then you're being dumb and pissy about it.
I don't think either of you are in the wrong, particularly. This is small stuff. But you could stand to have a straightforward, honest, mature conversation about the whole thing, like a pair of adults.