Ok, I am by no stretch of the imagination a dog behaviorist. Or kid behaviorist. I've raised both a few times over and this is my opinion.
Kids should be allowed to give the pup attention one at a time. You are trying to keep the pup from having a traumatic experience. Kids should be calm when approaching the pup. No running, screaming, etc. The pup just left his mom and littermates. He/she will be scared enough. Try and keep the house as calm as you can especially the first week.
Expand from there and they will all be best friends eventually.
Oh and My God, kudos to you. I can't imagine 4 kids and a pup.
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