Use the the internet to try and find free activities in your area so that you guys can get out of the house. Go to the park, see if your malls have kid play zones, look for museums with free days. That will help you feel better and in turn have more patience with toddler behaviors.
Your DD sounds like a normal toddler. Remember not to give in to her tantrums and ignore them as much as possible. If she hits give her a timeout. You really just have to wait out the toddler stage. My 3 year old is going on 4 and still has emotional outbursts everyday. She is all drama LOL Then I have a 2 year old who is less drama but gets into everything and loves to scream!! At least my 7 year old is calm.