tough call, especially with a kid along.

Your only options were to stay and hope you got better (maybe just spend a day in your sleeping bag, or sitting around a big fire), or leave.

One thing that you might have tried was to simply go out to town and get a motel room for a couple of nights, and see if you felt better, and if so, attempt to get a new entry permit and resume your trip.  Gives you a third option.

A friend of my brother's came out to Colorado to Elk hunt with us one year - he caught some kind of flu bug or whatever, and felt miserable (it snowed off and on) - we took him out to town and he stayed in a motel for 3 days, and when we went to check on him, he felt a lot better and rejoined us and at least got in 3 days of hunting.