Congratulations and welcome from one newbie to another!
It sounds like you are off to a good start. One suggestion I'd make is to be careful what you are cleaning up the accidents with. I'm sure you already know since you've trained another dog recently, that you shouldn't use household cleaners with ammonia in them to clean up pet accidents.
The ammonia in the cleaners tells the dog "pee here!".
The only thing I can think of to help with helping your older dog to adjust would be to only expose the older dog to the puppy after you have thoroughly tired the puppy out. I think that might help if the puppy is all worn out. The puppy may not get *quite* as crazy that way which could help make your older dog more comfortable.
Good luck. I'll look forward to reading about your progress!
p.s. Do you have any pics of your baby? I'd love to see them!