A few points.....
Start using a Kong, as you’ve said you will, but mix the dogs kibble with a little boiling water, so it turns slightly mushy. Then stuff the Kong, and freeze it. It takes a lot more effort and time to eat then.
Similarly, peanut butter or fish paste etc. Smeared inside, but be aware low fat peanut butter is harmful as often contains xylitol.
Thunder shirt and plug in are good, try a radio too. Is the dog crate trained? I’d definitely recommend it if not, but if you are not experienced in would help to get professional help to do this.
A professional can help you, but it is entirely possible a dog that is dog reactive on lead will not be if off lead, being on lead can make a nervous or anxious dog worse, it’s a vulnerable feeling for them.
Did you walk the dog with the empty pram before baby arrived? What was he like? If you didn’t, I know it’s too late now, but I’d highly ecommend it to anyone else pregnant and dog owning that could be reading this. You feel a muppet but it’s very sensible.
Also, a sling is a god send.
It can be done :) I have a pack of big dogs, numbers between 3 and 6. They have all walked nicely by the pram, or when I use a sling, I walked my dogs twice a day every day, 45 mins minimum from when my baby was three days old. Practice makes perfect, it’s great for yo and baby as you know, and if you build it in as a non negotiable part of your day, you will learn to find way.
I do feel like the crazy dog lady with two or three dogs each side of a buggy! Or five in one hand and helping a toddler cycle on a wobbly bike with the other hand. It all works fine until a puppy or youngster decides they want to be on the other side, crosses in front of the pram or in front of my feet and causes carnage idiot