Thinking about your kids problem, are we usually talking about sub-dermal bleeds or actually loosing blood volume due to external bleeds?
For the latter, there are products like Quickclot that will stop these fast. They are somewhat expensive, but there are improvised alternatives. There are two approaches to this. The first is a kind of volcanic rock that is pulverized, and placed in a oven at 125-150 for an hour or two to drive off moisture. If placed in a container that will keep it dry, when applied to a wound, will have an exothermic reaction that will cauterize it. It hurts! Mylar sealed w/ a curling iron is a good container for this and the next one. The second has to do with the exo-skellatins of shrimp. Go out and find a good deal on a bunch of shrimp for dinner. Chow! bring a bag and take home all the shrimp hulls. Maybe bribe the wait person to bring you a bunch more... wash/clean them out really good! Pulverize. bake at 125 deg for 1-1.5 hrs. seal as above. To use either, blot off blood and pour in.
The above is usually used for gunshot wounds. They work well, really well.
For the former - I'd be thinking about a BP cuff over the area of injury, but I'd be worried about cutting off blood supply to the distal limb for an extended period of time... Consult your doc on this... Transport time to the hospital, maybe. You can extend this by letting up briefly every 5 minutes or so... Being snowed in - not!
Hope that helps!
-t