I would be annoyed too if Dog 1 wasn't invited to go to the same places Dog 2 is. If the in-laws insist/ask that you bring Baby, tell them your concerns... namely that Baby is not as well trained as Stinky in terms of respecting space and property, which is normal because he's still quite young despite his size and is still in training. Say that you were okay with bringing him for mild training in other locations at their house - which you appreciate - in the past, but Christmas is a busy time and you don't want to have to focus so much on making sure he doesn't disrupt people/things on such a wonderful day. It would be more peaceful to continue carrying out the training on other days. However, if they really want a dog there, you can bring Stinky, who HAS been trained and would love the chance to visit the in-laws (because Baby has told her so much about it, maybe?). Have they even heard Baby bark? I ask because you say you think they're afraid because she barked at them. Bark worse than their bite, etc - and they are not, apparently, knowledgable dog owners because any true dog owner knows dogs bark! Especially at the door/doorbell.
I would also invite them to spend time with BOTH dogs at the same time. Either invite them to your house, or to a meeting at a neutral location like a park where the dogs can burn off energy and your in-laws can see Stinky away from the scary situation (barking at the door) and interact with them. That may help them warm up to her a little more.
My sister would not let me bring my service dog to her house for Christmas Day - for no reason I can think of, since my dog was quite well behaved and followed commands, and just wanted to be with us on a wonderful day. My parents had no such problems, and would insist that he come when it was held at THEIR house. I was sad when my sister unilaterally decided for all of us that her house - smaller, less room for entertaining/parking - had to be THE place for Christmas, and all protests were brushed off, and of course my dog could not come. And then she had the nerve to complain to my mother that I didn't "stay long enough" after presents were opened because I wanted to get HOME to my poor dog left alone. And then she got a dog and claimed that "two dogs would be too difficult" even though neither one were at all dog aggressive, and had indeed met and enjoyed one another's company (at my parents' house) - I'm still a bit bitter about that. So I do understand how it feels to have a pet be treated oddly by "family."