I read all the responses before replying so I wouldn't repeat. Here's my thought.
I teach 2 & 3 year olds and while I've never heard that time outs are inappropriate for that age group-- everybody gives them and unless you orchestrate it negatively I don't think it's any more negative than any other punishment-- I just realized I don't think I've ever actually given a time out to a 2 year old! Here's what I do.
2 year olds can understand reason once they calm down, so you have to sit him down and firmly wait for him to calm down before you ask him if he knows what he did and why it was wrong and what he can do to make it better. Usually a 2 year old can actually do that, though I don't know how young your 2 year old is. Then if you wanna do something like taking something away from him as his punishment, DON'T make it a bedtime story (unless it's bedtime) or anything that won't happen for several hours. 2 year olds need immediate gratification, so you have to take away something they wanna use right at that moment to be effective.
Yes, redirecting is best and easiest for mommy and kid at this age, but if he's doing something really MEAN or wrong redirecting won't cut it-- he needs to KNOW that his behavior is unacceptable! You can't just distract him cuz then he doesn't learn anything!
So here's what I do. When I have a student who's difficult I praise him at eeeevery corner all day long-- I mean if he so much as smiles I give him some sort of compliment. Then he learns to live for that praise and all I have to do is have a disappointed look on my face, or ignore him, and he knows when he's done something wrong and he feels bad himself without my having to "punish."
In terms of sending him to his bedroom, I think we all got sent there as kids and we turned out ok so I'm sure it's not damaging. The only reason I wouldn't send him there except if he's been acting up all night long and is being impossible-- is because bedrooms usually have toys and stuff and he may choose to play rather than to reflect. But you know what? When I'm mad I need to go to a completely different room to be alone too. Sometimes I need to flop down on my bed and cry and sit there for a while until I can be reasonable. So why shouldn't a 2 year old need the same?
I think you're doing just fine. Everyone has these situations. Oh and btw usually 1,2,3 then time out is best, not just one warning. 2 year olds have short term memories so 1 warning usually doesn't cut it. 3 are better. And usually if you start to count he'll get the idea by the count of 3 and then you won't hae to deal with any of it!
Good luck! I'm sure everything'll be fine!