I think it depends on a number of factors. The individual temperaments of the puppies is huge. But also the experience, management, leadership style, and expectations of the primary care-giver. Since I live alone, I really do not know what effect other members of a household would have on a pair of littermates.
I don't generally place littermates in the same home, though I have raised several sets myself without issue. I don't have a typical set up, and I have no one inadvertantly thwarting my efforts. I do have a pair of littermates out there, males, who are 2 1/2 years old, and it is working out fine. I homed the one puppy with the people and after about 2 months of almost constant contact with the owner, I went ahead and sold her the other puppy. So the first puppy had 6-8 weeks with the new owner before the second puppy came there. The second puppy remained in a litter setting with at least one litter mate and his dam until 16 weeks when he got his last set of shots and went to live with this lady and his brother.
She has a part-time son of about 7 years, and a fiance. When I sold her the dogs that was it, but then her X gave her back an older female, and her brother dropped his boxer into the mix. So, she now has four dogs. 3 young males and an old bitch, all altered, if that matters at all. The boys do not have any serious aggression issues, or problems bonding with people. The puppies split their favorites between the gal and her fiance. I do not know if there are any separation issues. But, when you have 4 dogs or more, the dogs are rarely alone. Separation issues often occur when a dog finds himself alone. I think that the dog you take with you, to classes or the vet, what have you, does not have that separation problem because it is with you and excited about what is coming.
If you take a dog out of a group, and then work with it in front of the group that is kenneled, the rest of the group are going to act nutty. It's like taking a child and feeding it ice-cream in front of a bunch of other children for whom ice cream is a rare treat. They may not jump up and down and bark, but what is probably going on inside of them, is what is going on with the other dogs/puppies freely.
So some initial carrying on will happen when one dog is removed to go anywhere. If this is a common occurrence, then once the car leaves the driveway, everyone settles down to their normal routine, if they are not totally alone. Some dogs truly do not do well with being on their own. Littermates or no littermates, some dogs, when separated from the other dog in the home, will freak out -- separation anxiety. If you bring a puppy home at 8 weeks, and you have an older dog, and for 6 months, they go everywhere together, or are together alone, or the puppy goes for classes or to the vet with you. All good. But then leave that 8 month old puppy at home alone when you take the dog to the vet, and if that 8 month old has that in her personality, that is where it will come out. Even a cat helps to make a puppy feel less alone.
And there is loneliness and separation anxiety. Loneliness might make a pup feel a little lost, and he will try to amuse himself by barking or chewing or digging, or even some depression. Separation anxiety, I think is where you get into dangerous behavior like scratching holes in walls or ripping out of crates in an attempt to escape. Maybe the two are the same, just on a spectrum. I don't know. Certainly the two dogs do not need to be litter-mates, or even close in age and acquired around the same to time for this to occur.
Most of my dogs I have known from birth, but none of them, even the ones that have lived for months or even years with other people are more bonded with the other dogs than me. I think maybe this is where pet owners, who have 1-3 dogs try too hard. People do not give animals the time and freedom to accept them, and rather, push themselves onto their pets.
What happens when you go with a group to a friend's or relative's home who has a dog you have never met? You zero in and try to engage the dog. The dog gives you his tail and gravitates toward the only member of the group who could care less about dogs. Maybe not all dogs, but it seems like most dogs do this.
And when we get a new puppy, of course we are going to be nuts about it. If a new puppy has another new puppy to gravitate towards, it may, I suppose, stay at a distance from the humans that keep trying to make it do this, or that, which are really not dog-behaviors: hugs, kisses, etc.
On the other hand, a crappy breeder who has to get to work every day, rushes through cleaning kennels and giving food and water to everyone, and maybe saves a few minutes to pet the puppies. And those pups crawl all over each other to lick her face, chew on her hands, try to trip her, and get hugs and pets. It's something like 7 parts trust, and 3 parts not expecting the puppy to produce golden poop.