I'm the only one with kids in my family, and every one of them has gotten the ass-kicking they've deserved at one time or another. My oldest is 26 and an Eagle Scout, aside from being one of the most self-centered people I've ever dealt with, he's a hard worker and unfailingly polite and respectful. My middle son is a hard worker, charitable and respectful. My oldest daughter is a wonderful person to everyone but her own family, and that is why she doesn't live at my house anymore. Sometimes we just can't win some battles. My youngest son, in spite of also being a Boy Scout and a really good kid, likes to tease his younger sister, and she is dealing with bullying issues at school. It came to a head a few weeks ago and I let him have it, pushed him around, yelled at him, kinda gave him a taste of his own medicine. I told him if he ever wanted to bully someone, go right ahead and pick on me or your uncle (who is 6-4 and 275#) and see where it gets you. I cannot tolerate rude people, never mind little brats that belong to someone else.
I remember as a kid, my dad's best friend from high school was up visiting and he brought his kids with him. The daughter was OK but the son was a holy terror and decided he was going to do whatever he wanted in our house. My father said something to the kid and he got the whole "you're not my boss I don't have to listen to you" crap, so then Dad turned to his friend and said if you can't or won't control the little brat, then I hate to see you go but take your kid and get out. The guy visited a couple times after that but always without the kids, and last I recall the kid was doing time.
As far as the OP's relatives, if those were my kids I would have burned every single gift in a big bonfire in the yard and forced them to sit there and watch it. And that they have 364 days to get their Sh*t together or it will happen again. No the kids are probably not 100% to blame but the parents are enablers and that's the worst kind.