Phew, Shoppingame! You have a lot on your plate! More than many of us grands could handle! Kudos to you for doing it at all!
As for discipline, I'm another one who feels that if the children are left in your care so often, you have the right to manage their behavior. In fact, IMO, you need to for your sake (you sanity) and theirs (their safety, etc.) It is said that kids think the world is going to be like their parents. But if a GP is the one caring for them a large chunk of the time (as you are), then some of their ideas about the world are going to come from the GP. So I believe the GP needs to educate them to appropriate behavior as much as the parents do. I wouldn't say this about, say, a GP who sees the GC once a week or the like. But this is a matter of 5 days a week for long hours.
Besides, a GP can't just stand there and let her GC hurt each other, etc., can she? I've watched my DGC for long hours, now and then. And if I just let them run wild all day and hit each other, etc. DD (their mum) would be furious!
Granted, I agree that a 1-yr-old mostly needs to be distracted or removed from a situation, perhaps w/ the word "No" being said, but not always. Distraction can also be good for a 3-yr-old, IMO. But if she's about to hit her brother, IMO, you need to pick her up and move her away before she can. And maybe separate them for a while if you have a way to do that.
I, too, am wondering where the father is and whether or not he gives the kids any attention. Also, I agree that it would be a good idea for you to spend as much time w/ them as you can when they are at your house, reading stories, playing games, etc. But I can see where that might be exhausting. Is it possible the parents can afford nursery for the 3 for a few days a week or a few hours a day, as others have suggested? IMO, that would be a big help.