Well, you can't raise a child to be afraid of being hit. Sorry, I don't buy it. And it's clearly not working. It teaches kids that it's okay to get so angry that you can't control yourself - and that's exactly what his problem is.
Your grandson is CLEARLY exposed to things you (and perhaps his parents) know nothing about. He's learning the "I'll shoot you" language somewhere. So, I'd ask first if his TV and computer game usage is being strictly monitored. I'd also ask who he's exposed to (family, close friends, neighborhood kids) who are teaching him this language and letting him figure out that it works.
And somehow, he's getting the idea that having a tantrum works. So, unless he has a major oppositional defiance disorder (and maybe he should be evaluated), he's finding, on some level, that tantrums and screaming work. The standard thing with a tantrum or screaming is to ignore it. That means, don't respond immediately by taking away things or, God forbid, spanking. It does mean, though, to pull the car over, park, and get out, leaving him screaming. Stand where he can see you so he doesn't feel totally abandoned or unsafe, but out of earshot. Tell him you'll get back in the car and start up the trip again when he stops screaming. Or, it can mean to stop dead in your tracks in a store, at home, or wherever, and tell him you cannot hear screaming or you cannot understand yelling, whatever words you use (but be consistent). It means putting him in his room, saying he can come out when he can be quiet and talk normally. If you're out, it means leaving the store, the park or the playdate if the first warning doesn't work, putting him in his carseat with a few terse words ("We don't scream. If you do, we go home.") and then NOT talking to him or engaging with him at all until he stops. Depriving him of attention defuses the situation, even though it's hell for a week or three until he gets the message.
I doubt very much that this is what your daughter is doing. If she is, however, and is doing so incredibly consistently (which I doubt, since she spanks), and if he's still out of control, then he needs to be evaluated.
A school cannot keep a child in a program if he makes threats. That's not acceptable language. But a school should also have people with some background in behavioral issues and early intervention (if he needs it - they should be able to tell). By the time your daughter gets to the school, it's way too late to punish the child for what he did. Consequences have to be immediate.
Some kids need a head's-up before they transition to a new activity. So if you walk in and say, "Clean up now, we're leaving," it sometimes gets a reaction. So a 5 minute warning, or a timer, or things like that can help. "When the timer goes off, we will start to clean up, and then we will do XYZ." If you tell a child this age that he needs to do X or he won't get Y on the weekend, that doesn't work. They can't defer like that, and they have little or no sense of time.