My kids are too little to have yet experienced this, but I wanted to pass on something that I read in a blog that really stuck in my head, on how a mother observed how her daycare handled this type of situation (with younger kids, but maybe it will work for yours) --
When a child cried because he was being excluded from a group of kids, the worker asked the kids what game they were playing. They were playing some game involving the San Francisco bridge. (No clue what that was.) And she said, oh, well, don't you need a toll taker? Bobby, (the one being excluded), why don't you be the toll taker? And miraculously, all the kids accepted Bobby as the toll taker, and Bobby was no longer excluded. I could envision some kids going "No, I want to be the toll taker!!" But then you could suggest that they all take turns, or that toll takers only wear blue (Bobbie is the only one wearing Blue), so Bobby hss to be the toll taker.
There are a few girls in my neighborhood who are 8 and 9, and a few are totally into the "you can't play with me" mode, excluding one or the other at various times. I was keeping my eye on my little guy, and they were playing school one day, and I wish I had read this blog, because I bet they needed a principal for the school. I do feel that at that age, you need not "tell" them what to do, simply because that won't work, but I think you can set a bit of an example. My saying, "it isn't nice not to let her play, you really should let her play, how would you feel, etc." didn't help at all.
I would never have come up with something like that on my own. No lectures, no sentences beginning with "you have to"...I think kids shut down and quit listening sometimes when sentences begin like that...and the problem was very neatly solved. I need to remember to ask my daycare how they handle situations, because there is a wealth of very valuable information to be learned there. Many have backgrounds in child psyhchology, and can suggest age appropriate responses.
I would be concerned about the locking of the doors, I would be afraid that something would happen to the kids, and then you wouldn't be able to get inside, so I would mention that particular suspicion to the sister-in-law, just to try and avoid that from happening.
And if the behavior doesn't change, I do like the suggestions about simply not having the play date with the cousin engaging in this behavior. I would come flat out and tell him if he persists, that because he is behaving so nasty, you will not come over until he can be a better host and that he is not welcome at your house, either. At six, he should understand that. I would say, you may not like my son, and you don't have to, but there are rules about how you are supposed to treat guests, which if you can't follow, we won't come over. See if that helps.
Good luck! I fought with my cousins like cats and dogs growing up, and the only time that adults got involved was when there was blood, but we love each dearly now.