It sounds like you have an active little boy. My first son didn't nap at all, but 10 minute power naps since he was born. But when he turned around 2 he needed a nap and finally started taking them.
So I have been where you are to some extent.
Something that stood out to me was that is the most critical I think is that it sounds like he is getting away with whatever he wants. You said he gets out of bed repeatedly and messes up the room and kicks the door, so you eventually (after trying to be stern by ditching the plan) let him out (and he gets what he wants) but because he did need a nap but didn't get one then he falls asleep at the table.
He is trying to rule the roost, and being the good mother that you want to be, you don't want to hurt him or crush his spirit, so you give in. I was just like that too, trust me. And my first son made all the decisions without us even realizing it. So I'm not blaming you at all. It's easy to fall into that without realizing your doing anything wrong.
The first thing to understand with any parenting technique is that whatver you do, you are "Training" your child to respond in either a good or bad way. By letting your son mess up the room or kick the door without any stern consequences, and then letting him out of bed, you have "trained" him that his behavior will eventually let him get up. That kind of behavior should not be tolerated at all. I firmly believe in spanking, as I have seen the good benefits of it and it does not make your child angry or become abuseful as some skeptics say. But if your against spanking, try something else. Its hard to put a 2 year old in time=out when he's supposed to be in bed. But you could firmly pick him up, tell him, "NO, you may NOT get out of bed. That is unacceptable. Mommy told you to stay in bed and go night night," and leave the room. The second he gets up again, go in and pinch his thigh, or a little piece of skin on his arm with just a tiny pinch. It doesn't really hurt that much and it isn't as invasive as spanking, yet it gives your child a bad result for his actions (and works great! Many mothers I know use this) and after a few of those your son will get the idea that you mean no monkey business anymore. He will eventually have no more pay offs for acting that way. He will get nothing out of getting up and destroying the room or kicking the door. When he realizes there is no other alternative, he will go to sleep and if your consistent with this method, you will have "Retrained" him that what you say, you mean, and he is to obey you because your the mother and he is the child. If you do believe in spanking, then every single time he gets out of bed, or gets out of a laying positiong (if he's sitting in bed screaming at you, or destroying the blankets) go in, sternly tell him with a calm voice "I told you to go to sleep. This is a no no. This is unacceptable. And swat him once on the bottom or the bare thigh lightly with a spoon just enough to barely make it sting a bit. It hardly hurts. You can try it on your own leg if you like to get the feel of how hard you think is right. And this works the best. You'll have him trained within 1-3 days by doing this very consitently.
The book all my friends use that has taught me all this great stuff is called, "To train up a Child," by Michael Pearl. Its a great book. I had no idea that everything I was doing was the wrong things and was making a monster instead of training him to obey lovingly.
Wish ya all the best~
H.~
SAHM of 2 boys, Rylan (4) and Rory (2)