Aside from the age of the puppy (which I hope is a typo because one month is far too young unless something happened to the mom), it sounds as if your older dog has the idea that it's her house, food, etc, not yours. The barking at strangers is a good clue (along with the other behavior) that she feels it is her job to protect the house, and she is doing her job with the puppy. As "leader", it would naturally be up to her to decide who gets to stay and doesn't. The temptation is to be even more loving and generous to your original dog when it "looks" like a jealousy issue, which would only reinforce the behavior, telling your dog you approve of her bullying the new puppy.
I'd remind your older dog (gently and lovingly of course) that you are the boss. Things like always going through doors first, making her sit and wait a moment before giving her food, never letting her walk in front of you on walks and basically not allowing the dog to demand any behavior from you (like nuzzling your hand to get patted)...all serve to get the message across that you make the decisions in the house. Your dog should relax and feel a lot more comfortable when she's certain that you are in charge, and not her.
The down side is you've had 9 years to let her think she's the one in charge, and it might take a while to convince her otherwise and consistency is crucial. There are many great books and web sites with information about the heirarchical way dogs relate and how to establish yourself as the leader...once you do nearly everything is much easier. |