Hypothetical questions here ... does she think she's better qualified to take them camping or does she think she's the more responsible parent? Or both?
Either way, this is extremely hypocritical of her. Sounds like she wants to be in control, at all times or at least have the upper hand.
It's great that you kept your cool about it though. I know you've been struggling with that. Treat her as you would any Tom, Dick or Harriet at the office ... with professionalism and diplomacy.
Back to the camping... I don't think your S7 is too young. S3 may be (depends on where you go) but certainly not for a camping trip in the backyard! Pitch the tent for a night out at home when it gets warmer!