no kids, but there is an eight year diffference in the age of my sister and I and since my parents divorce there were times I was more like her mother than sister. She is 14 now and will go to the local amusement park by herself all day with a group of friends, I (or my parents) would never let her go off by herself, even if we were in the park, too many things can go wrong, even with one other person it is ok though. The same would apply to WDW, if the situation were to come up, my sister is very responsible but I would never be able to let her go by herself, with a friend for a couple of hours sure, if I was in the park and we had meeting time every couple of hours, but not by herself.
At your kids ages, it would depend on their maturity, if I thought they could handle it I might let them go together for 1 or 2 hours, once then see how they handled it, with one of those radio things, then go from there, if they met me on time, were ok and together, then maybe do the same thing once a day during the trip, no more than that. Even then I would be so nervous.