You could try telling him to stop/not go outside/do this or that yourself, as some suggest below, but frankly -- if his parents are as controlling as you note, I suspect they might go ballistic at you for "correcting" their child in their presence. That'll really make Christmas Eve fun. You can get him to behave when you're babysitting him, which is great and indicates he is capable of listening and controlling himself for you, but in the high-pressure situation of a holiday at the grandparents', your influence may be greatly lessened, sadly, by his own parents' overbearing (or too-slack) presence.
To salvage the holiday, I'd go with the idea of a new tradition. Go to your in-laws for only part of the evening then take your own sons out to see holiday lights if you have good ones in your area. Or if you're religious, add a Christmas Eve service (there are cool ones aimed at kids and tweens!) to your night. Or if your sons love movies, take them out to a film for part of Christmas Eve (some people are going to freak at that suggestion, but I know families who do that, or who alternatively watch holiday movies at home together on Christmas Eve -- there are plenty of comedy holiday films your boys might like).
In other words -- take the focus off We Must Be at Grandma's Or It's Not Christmas Eve in your minds AND in your in-laws' minds. It's up to your husband, though, not you, to see how this is going to sit with his parents. They may understand. And he does not have to tell them "This is because of little Bobby's wild ways" or the grandparents will be more irritated with Bobby than ever, and it's his parents, not the kid, who are to blame here. (Yeah, there IS blame in this world, so let's assign it where it belongs here!) I would just tell the in-laws that you ARE still coming to them but, because your boys are getting older, you are building some nuclear-family-only time with them while they are still at home -- they'll be gone soon enough (true).
Placate the in-laws by adding an extra visit over the holidays, maybe stopping in for dessert on Christmas Day. Or why not have the grandparents over to your house on Christmas Day for a few hours without SIL, BIL and Bobby?
Frankly, you can use your own kids' ages as an excellent, and very real, reason to cut down the Christmas Eve time with the extended family, and you can make the grandparents happy by seeing MORE of them at other times over holidays. Christmastide is not just Christmas Eve, and Thanksgiving dinner tastes great the next day if everyone has a laugh about it and isn't obsessed with dates on the calendar.
As for poor Bobby -- if you can, I'd offer to babysit him a little more. You seem to do the child good. I'm saying babysit because the presence of his mom and dad, and their hot-and-cold, conflicting parenting style that's lax one minute and strict the next, would only undermine the good you do him.
For Christmas, I'd give Bobby a trip to the zoo or some outing where he's with you but not mom and dad. Give him a TON of praise when he's good, too.
If you just must do the Christmas Eve thing, try bulldozing into the evening with a lot of things in hand for Bobby and your boys to DO in another room while the adults talk and visit elsewhere -- videos, small and inexpensive handheld video games, a small Lego kit if he likes that, stuff to keep him occupied. And more stuff for when the initial stuff wears off. It's not ideal but it's a defense mechanism for you as the adults. And again -- praise him long and loudly when he's good and just leave the room when he's not.
By the way, I'm sorry to see so many folks here rushing to insisting that "he must have a sensory issue/other problem" when you've already noted for us that he does not. And the way he will settle when you babysit him indicates that he IS capable of decent self-control.