First- Hugs to you!
2nd- please have him tested for Autism. While destructiveness and general not listening is a common 3yo issue, this seems a little more. The touching everything in sight is what concerns me. He is testing your boundaries.
3rd- if he tests negative, put him in a good pre-school. That will get him out of the house and into a consistent, structured environment. It will help him learn to follow rules and play well with others. Full time day care may be a possibility, even though you are a SAHM.
4th= age 3 is THE WORST age. 2 has nothing on 3.
My middle one was very resentful towards his younger brother (I have 3) and it still has not ended, but it has lessened (they are now 8 and 4). It has helped that they share common interests and spend time away from each other everyday (in school). They may never "like" each other.
The only bad thing about "firsties" as I call them, is that they have had all the attention for so long it is hard to give it up. He is trying to get you away from the baby and is using bad behaviour to do it. Be firm with him and let him know who is boss. He is now old enough for time out to be effective if it is used properly. He is also old enough to understand that there are consequences for his behaviour. Take his movies away. Take his play dates away. Yes, it is harder on you than it is on him, but he needs to learn to behave.
Schedule a time where someone can watch the baby and you and he can go out and do something just the 2 of you. It may help. Try to do this once a week. Maybe even put the baby in Mother's day out once a week and give you oldest your full attention on that day.
Good Luck!