My daughter and I are in exactly the same boat. 1st, you have to choose some of your battles. If its something really not important, then let it go. That may get some criticism, but when you are by yourself parenting, its hard. Lucy used to throw fits that she would not get into a cart at any store, she wanted to walk. What I started doing was talking to her as we entered the parking lot. I explained that I would let her walk like a big girl to the store, holding my hand and then she was going to get in the cart with no fighting. She argues in the car, but I won't back down. Tell them exactly what behavior you expect, if you know there are certain things that trigger a fit. She still put up a little fuss, but she got in the cart. Now, I hardly have a problem at all.
I also started using what I call the choice method. Right when she seems to be getting upset, I give her a choice. They may niether one be what she wants to do, but you are giving her a choice none the less. Sometimes, if we're out, I give her 3 choices and the 3rd is to go home. This has really seemed to work with Lucy.
Also, I saw a show a while back about Toddler speak. It explained that they get so focused that what we are calmly trying to say or screaming at the top of our lungs about just won't get through. You might notice that your daughter is repetitive in things she says and does...do this with her...repeat yourself in short phrases, in a firm voice. Be on eye level with them. This has worked for me too.
If you want to contact me, feel free, ____@____.com. I'm a single working mom with an almost 3 yr old daughter, so I'm sure we would have a lot to talk about!