Holly behaves differently when my wife, Judy, is with her than how she behaves when she is alone with me. When Holly is with me, she is open and friendly with strangers. I have made it a point to bring Holly to places where there are lots of people with whom she can interact. However, when Judy is with us or when Holly is alone with Judy, she is shy and recitant with strangers. This is even true in venues to which I have brought Holly previously.
Unfortunately, Judy has never seen Holly interact with strangers when she is in her more open persona and really doesn't believe that Holly behaves that way. When Holly is with Judy, she will often retreat behind her in the presence of strangers. When she is with me, Holly will sit and let strangers pet her and will lick their hands if offered.
Our previous big dog also acted differently when she was with Judy than when she was with me. Sara was a big and imposing German Shepherd/Golden Retriever cross who weighed 85 pounds and had long wolf-like legs. She was a happy go lucky dog when she walked with me but, dialed into a protective mode whenever she walked with Judy. Sara would always be scanning the immediate vicinity for danger and would intercept anything or anyone she thought was a danger to Judy. She would not be vicious or aggressive in her protection but, would let the interloper know that Judy was under her protection.
It's funny how both dogs reacted differently when with Judy; Sara becoming protective and Holly becoming rather shy.
I think dog behaviorists and trainers would tell you that the dogs see you as their "pack leader" and therefore can relax around strangers. They know you are in charge and they don't have to protect themselves or you.
But with your wife, they are assuming the role of leader/protector because they apparently believe they are in a position above hers in your pack. At least, I think that's the way "Pack Theory" goes.
Do you do more of the training with Holly? Our trainer (who is also a behaviorist) encouraged my husband and I to both spend equal amounts of time training Peri. And taking her outside, for walks, etc....
After a few obedience classes (we took her together) and trading off duties (even going home for mid-day walks) I would say Peri views both of us as pack leaders and acts the same no matter who she is around.
We have the same situation, only the roles are reversed. Guinness is great with me on walks, but not with my husband. He won't heel for my husband and he "fear barks" when he sees strangers. With me he does a perfect "heel", and I've never had a problem with him barking. I'm the one who has done all the training with him, so it's probably not surprising. I'm also the one who feeds and grooms him, so I think he sees me as the "leader". My kids have always said that I "mean business", and Dad "not so much" - he's the fun one. I think our puppy has the same idea. LOL
Ned is also different with Skip and I. He is more cuddly with Skip and walks better and behaves better on a leash. Guess who trained him?! Guess who forces grooming?!
I found out that our 16 yr old lab that doesn't like other dogs, doesn't actually mind other dogs. She just doesn't like other dogs around me. When we left her with someone when we went on a trip I told them not to let the kkids wallk her and not to let her off leash as she didn't like other dogs. They found this not to be true. They started walking her and found she didn't react at all to other dogs. So much so that they let the kids walk with the leash too. I was shocked. My son took her to the dog park with Neely when he first took him and she was fine there too. She does get a little whiny and nervous if they play too ruff but usually just tries to alert us to that and tries to get in between the dogs while telling us its too ruff. We just have to pet and and calm her. She doesn't seem to mind other dogs so mush anymore with me either. I think she thinks her focus is as mommy to Neely now not me.