You are an awesome sister and Aunt!
When she picks him up, she could give him a piece of fruit, a bag of raw veggies and plan a way that they can sit down for dinner as soon as possible (hints below) and then bathe him. Make sure all of this is done in a very quiet setting. No running around, no TV no cell phone interruptions. This way, he will not feel like he is missing out on anything.
Pop him into a warm bath with quiet play in the tub. Have your sister speak quietly with him. Have her use strong wipes on his body like a massage.
Again make sure he cannot hear the TV going, cell phones ringing.. lots of laughing and talking going on around the house. This will just make him think everyone else is having a party without him.
Their room should be darkened. (Black out shades are great, I used to hang quilts) quiet music or a sound machine. Have her read quietly to him and then and then he should be asleep by no later than 8:00 (7:30 would be perfect for a 2 year old)/ This needs to be done every night by whoever the caregiver of the moment is. He needs something to be an exact schedule in his life. This can be it.
If he gets out of bed, he must be returned every time and told. "it is sleep time.".
Tantrums for a 2 year olds means, stepping over him and ignoring him. Just say, "when you stop crying I will give you a big hug". If you see the signs of feelings coming on, give him the words. "You look frustrated, you look like your feeling hurts, you look like that made you mad." Pick only one so he can beginning to recognize this is what he is feeling. You all may need to go to your own rooms and let him deal with those tantrums on his own.
You can try a time out chair. He will need to sit in it for 2 minutes. But he may be a little young.
You all may need to pre-plan meals for the week. I like to grill a lot of different things all at once and then freeze things so I can just microwave them. Hamburger patties, Chicken breast, Italian or polish sausages, hot dogs. Sometimes, I will purchase a huge amount of ground Turkey or beef and cook it all up at once drain it a nd store it in 1 to 2 lb lb in a ziplock. This way you can season it for whatever you are going to eat.. Tacos, sloppy joes, whatever..
Always keep on hand pastas, jarred sauces, fresh veggies, fruit, salads, buns, instant beans, rice tortillas (also freeze great), yogurt and shredded cheeses. This will make putting together quick meals so much easier.