I know each child is different, but as I read the entry, the main thought that came to mind is to find out how much time does she spend playing with him?
The reason I ask is that I notice my daughter (5.5 yrs old) will get much more out of hand if I have been busy with projects and not giving her the attention she needs. She's always done this. Now that I have a second child, I notice he does the same thing but not to a very extreme level yet. Generally speaking, though, they are great kids that are very well behaved and I give them plenty of attention, but there are times I get a little too focused on something else and need to refocus and give them attention. Whenever they start getting a little more disobedient of upset easily, I quickly think through how much attention I've been giving them and when I adjust it and sit and play with them, they respond much better and are much more willing to obey.
I do also discipline them on top of that, but I always make sure to be doing my part to help them not react to anything I might be doing that is causing them to feel upset.
I'm betting your sister works (kind of seems like she'd have to in her situation!), so anyway, that's what I would suggest...make sure to sit and have one on one time with him and give him her undivided attention. Then add disciplining on top of that after she makes sure he's getting the attention he needs from her.
In case this sounds negative at all towards her, PLEASE know i don't mean that at all! I can't imagine how difficult it must be for her and how frustrating this must be. This is just what I've noticed helps me.
Hope she is able to figure it out!