My thoughts:
1) It seems to me like 11 years old is kind of old to still have a belief in a literal Santa. What do others think? At any rate, my suggestion would be to take the 11-year-old into the conspiracy. There's no literal Santa--it's Mom and Dad--but Santa represents a spirit of joy and giving and selflessness that anyone can share and believe in. So, maybe the oldest kid would like to help set up "Santa proof" for the younger kids, like reindeer hoofprints in the living room or something, thus passing on that magical feeling of joy to the little kids.
2) I felt the advice was phrased a bit confusingly, kind of meandering, when more practical suggestions would have been helpful, and she gets into a digression about whether he might be on the autism spectrum, which is really something for his parents to deal with. I agree with the advice to refuse to be alone with the kid and tell him flat-out that it's because he keeps grabbing the writer. Does a year seem like a long time for a kid to fixate on something like this? Part of me wonders if he is doing it precisely because he gets a rise out of people about it, so maybe they should focus less on the height issue and more on, "Grabbing and pushing people is wrong, you are grounded, go to your room." And interrupting people is wrong, if I have to tell you three times, you're grounded. Or whatever punishment scheme the family uses. Obviously the writer has to make sure the kid's parents understand her discomfort and have her back on this, since they are the ones who will be punishing him. But no, like, yelling at him or otherwise causing a scene he might enjoy. I would try that first, anyway, and see if that shakes him loose from this behavior.
3) I don't have a spouse or kids, so I don't know what you do if you disagree with your partner about a parenting decision. In an ideal world, I would say, "Why does Mom have to solve this, when Dad caused the problem?" I would point out to Dad that the kids might be upset about the stocking colors and he needs to fix it. If he didn't agree it was important, then I would leave him to deal with any tantrums or meltdowns that occurred because of it. But I don't know if that's really a practical answer. Instead of buying new stockings, perhaps the parents could involve the kids in super-personalizing their stockings--like the kids get to glue pompoms and fabric pieces onto theirs, while Mom and Dad's remain plain. Then it would be like, the kids' stockings are decorated and the parents' stockings are plain, which might make more of an impression than the underlying color.
I guess this means I do agree that the color differential seems potentially problematic--in and of itself in an ideal home, it would not be a problem, but there will always be unfair things in life, and a Christmas stocking is a very potent receptacle for symbolic resentment. Like Kid 1, in 20 years, could articulate the immense pressure he feels as the oldest child to follow in his dad's footsteps as an accountant, even though he wants to be an artist, and he hates that red stocking that's just like Dad's, and always envied his little brother, who was allowed to be more free-wheeling and follow his dreams, and his stocking was GREEN like no one else's! You know, it's not about the stockings, it's just that the stockings are tangible evidence of other forces he's been feeling his whole life. Why not try to make things as fair as possible for the kids when you can, knowing that there will be many times when you can't help but be unfair?