Good reply LR. I would ask if your puppy is being crate trained? Never use a crate to punish, start slowly by making it a happy place, food, treats, rest. If your puppy is crate trained then when you are prepping food in the kitchen the pup can be sent to the crate and given a treat and can stay there until the kitchen work is done and food removed. No more crying for or jumping up on the counters for the food. The key is making the crate a happy place though, give it a command/name -go to your crate - help that to happen nicely and the dog will learn to go there on command eventually. When the pup is a little older you can work on making him behave better around the food, once he understands more commands and words.
When you have the kitten and pup together, do you keep the pup on a leash so you can make a quick correction without necessarily removing him completely from the situation? Good luck to you, you've bitten off an awful lot with two little ones.