Awww,,,, you are showing the tell-tale signs of being a Grandma. It's okay.... it's only natural to feel like this!
He is misbehaving, all right. Do you have a crib? A two-year old does not know what a "time out" is. Just tell him if he doesn't do something, "do you want to go nite-nite?". After asking him (reminding) him 3 times, just plunk him in the crib, turn out the light, and leave him for a minute. He'll get the hint right away. That's all that I did with my 2 yr. old nephew....
Toilet training? Oh my god, you poor, poor woman! Those stinky, stinky, stinky diapers!!! Bleah! That is just too much!!!!
When he throws his food around, whatever, meal time is over, period! Tell him no more until the next meal. He'll learn in one heck of a hurry what meal time is all about!
One more thing - make sure to play with him, and laugh with him. He needs not only that type of discipline, but immediate love and feeling like he's not the worst little kid in the world! Don't make a big deal at all over his mis-behaviors. Just make up your discipline, stick to it (remember, he's only 2 ! ) and don't worry too much.
Spanking? I suggest taking his diaper off and giving him the tiniest pat on his butt imagineable. That'll make him cry, and it will not hurt him one little bit. That is, if you need to.... a wooden spoon? No, put that away. He doesn't need to feel that kind of pain at 2. He is going to be a bit bratty, and scared, seeeing as his parents are away. Please keep that in mind before hurting his little behind. He doesn't want to drive you nuts - but he is; so, grandma, you need to take it... (I know it sucks! )
Good luck, and try not to stress too much.