I am by far no expert on the matter, so please take my advice how you will.
It seems like both of you are scared or nervous of your puppy barking excessively at other dogs.
So for example, I am about to take my puppy into Petsmart, and I'm really nervous she's going to bark like crazy, right away she is feeding off my nervous energy, when we get in there, and she starts barking, the nervousness and embarrassment that can occur will certainly not help the situation.
I like to think of projecting energy with a simple example. My nephew falls and bumps his head infront of me and my sister. He immediately looks towards us. If for example we both make a sad face and said 'Ooooh hunny, are you okay? Come here my baby, let me kiss it better.", there is a good chance he will start to cry because he can sense something bad just happened. If when he turns to us we say in a calm cool voice 'Its okay, you're fine.', odds are he will just get up and keep playing. Obviously this is assuming the bump isn't too excessive.
Puppies in my opinion are the same, if when the excessive barking starts and you just get nervous and anxious hoping its all going to go away, it'll probably only get worse. And this starts from the second you get out of the car in the parking lot of Petsmart.
I encourage you to work on what type of energy you are sending out, I know its probably a lot harder than it sounds, but it could help.
It goes back to a bigger picture of becoming the alpha male in the pack. If your puppy knows you are the leader and respects you as the leader, then when you redirect him from barking he should stop.
Obviously a lot of the above would only happen in a perfect world, but it definitely could help.
I remember watching an episode of The Dog Whisperer, and this one lady's dog would gnarl and bark at any people passing by. When Cesar walked in the room alone with him, he was absolutely fine, the dog layed at his feet and was submissive.
The second his owner walked in, she had this fearful look on her face like she was saying 'It's okay hunny, he's only here to help.', immediately the dog started gnarling and barking. It was an amazing thing to see and Cesar was able to show the audience exactly how projecting negative energy can encourage bad behaviour.
I really hope this helps.
Also, I am not implying either of you are bad owners in the least bit, I'm just simply stating what I think could be the problem and what could possibly help.