I get why you think she way entitled, demanding you walk an extra half hour to get back to your car and refusing to listen to your explanations as to why it wasn't feasible. I get the feeling that, at that moment, every one was a little on edge. As a dog owner, I get why you didn't want to place the additional stress on your pooch, but as a parent I can also understand asking someone to not freak my kid out.

Perhaps there could have been some middle ground. eg could you have waited a short way down the other trail until the family had passed, then backtracked and continued down the original trail you were following? I'm saying you had to go the whole way, just far enough for so both groups could have kept out of each other's way.