There is a lot of good advice in your post. On the occasions when they won't do something which you know they are capable of, have you tried altering the result of their refusal?
For instance, when the 4 year old refuses to put on his shoes to go somewhere, then tell him that if he doesn't put on his shoes, then he won't be able to go.
When the 7 year old refuses to pour his own drink, then tell him he'll have to go thirsty. He'll soon change his mind if he really wants the drink.
That way they are learning self-reliance as the only alternative is to go without something that they want.
Oh yes, we do that with the 4 year old. He likes to go with my husband to pick up our older son from school, and if he's refusing to put on his shoes, we usually tell him that he can just stay home. They usually has him moving. If we are already running a bit behind, however, it's sometimes easier just to slip them on for him. I know it's bad though...something we are trying to move away from more and more!