C.P.
Our son was also 3 when our 2nd child was born. It was a rough time! He was doing all of the things you've described... it was horrible. He loved his new baby sister, but the bad behavior, bad words, hitting... just kept getting worse.
You need to be very calm. Read the 1,2,3 Magic book!
Once we started following it to the letter, his behavior improved dramatically right away. Basically you don't show any emotion, but simply count bad behaviors. "1" is the first warning. "2" is the second warning. "3" gets him escorted into your designated "time out" spot. We use his bedroom because I literally have to hold the door closed to keep him in there, all the while listening as he trashes the room and/or pees on the floor. It's loads of fun. But it works! Now when I say "Alex, that's 2" he stops what he's doing almost instantly every time. It's totally amazing. But the book has loads of other very useful info that you should read. I cannot recommend it enough.
I also agree with you that age 3 is very hard to manage... But big life changes during that year make it extra hard! We also moved during that time... man, I wouldn't want to go through it again for anything : )
The good news is that you will get through all of this. And you should spend some time alone doing things with your son. We've found that putting baby to bed at 6:30 or 7pm is so perfect because then we have lots of time to read books with the 4 year old before bed. It's great to have that time alone with him. My husband also takes him out on outings all the time, even if it's just a walk to the kwikimart for an ice cream bar before bedtime or baseball in the back yard for 20 minutes. It all makes a big difference.