The puppy is too young for harsh corrections, you could even make him leery of small children if you go correcting him with a prong collar when he encounters one. I do not particularly like the kneeing of the puppy.
This is a very young puppy. But that does not mean he cannot learn. The first thing he needs to learn is that he is only rewarded when he has Four on the Floor. That goes for treats, for praise, for pets, for anything. If all four paws are not on the floor, no positive attention at all.
Time outs in the crate. I think that the crate should be only used positively. However, you kid should not have to go through the next three months being jumped on. When there is a little to much exhuberance going on, I do not see why you cannot place the puppy in a safe zone for a breather.
My parents have a pet yard set up in their living room. The pet yard is for the kids, not the dog. The grandkids have toys and such in that area and the dog respects it if the kids are there. The kids can always go in their safe place. For a puppy I suppose that could work in reverse. You see the four year old is out of his comfort zone, so scoop up the pup and put it in the play yard or x-pen. It is not a punishment, it is more of a safety net for both dog and pup.
If the pup only has problems with the four year old outside, maybe there is too much going on outside, kids running, screaming, etc. Maybe it is better to have the puppy not go outside with the four year old until the puppy is a little better controlled.
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