Congrats on your new puppy!
I think you are on the right track, time is the best cure here. He will begin to understand you are his pack (including your kids) and will feel more and more secure to wag his little tail
One suggestion I have is to take some time everyday to sit with him and your kids and teach both how to play. Teach your kids that they are the owners too, taking ownership and having a "job" is very important to my kids (plus they love telling Lily to drop her toy, she's the only one they can boss around like that lol). You could also get the kids to feed him if he doesn't have any food aggression ??
anyway good luck and pls let us know how it goes!
