Two is a hard age, but it can be a lot of fun! I have a two year old right now as well, so I can totally relate!
I think the biggest thing you can do when you react, is to react how you want to model behavior for him- don't yell and scream when he loses it- but talk softly and tenderly. Sometimes he might just need a nap too if he is melting down. One thing I learned with each of my kids was if they are screaming- just take them to bed- they usually ended up crashing! I wouldn't ignore the behavior as that makes it acceptable. He might be melting down each time you correct him because he is a little sensitive- mine is like that too. We still correct and say 'no hitting' but then we redirect and say "instead of hitting, let's go color over here- this is how we can be gentle with each other" or something like that.
Don't get frustrated if it doesn't get fixed over night- two won't last forever and sometimes it just takes some time to work those issues out for kids!
My son turned 2 in August and he's getting like that as well. My son never really was a stubborn child when he was a newborn and an older infant. All I can say is if you're concerned, then maybe you should talk to your child's doctor and see if it's more to it than that.