What to do (if anything) about my dog's confusing reaction to our new puppy?

I take my older dogs outside and then introduce the new puppy outside so if anyone has to pee they do it outside. It takes older dogs a while to warm up to new puppies, usually a few months. The baby teeth come out between 4 and 6-months-old and the puppy gets a little bigger then. While I expect them to work some things out on their own, I step in when anyone does a behavior I don't allow. Be fair, if the older dog starts it, correct that, if the younger one starts it, correct that. I use the command "shame" so I point at the one who started it, snap my fingers, and use a command "shame" when they behave, I praise them. I use Charlee Bears for potty training, so when the new puppy goes potty, she gets a treat, and so do the other dogs. The puppy learns to share treats and that she is not more important than the other dogs. I do everything as a group. Potty, leashes, training, walks, play time, combing hair, it is all done as a group. You can give an older dog extra attention while you are waiting for a puppy to go potty. While I expect them to work some things out, I correct any behavior I don't allow, the second it starts, they are each others pack now, but it is my job to step in and correct any behaviors I don't allow. It just takes time but you get out of them what you put into them, so hang in there.