Hi there. My son is 26 months old so I am/have been experiencing similar behavior. At first I was really stern with him, but that didn't produce good results.
My advice:
Continue to use time outs for hitting or other violence or "rule breaking". Make sure you have specific rules and only use time outs for those. In my house it's like: no hitting/kicking, no spitting, dont throw your toys/food, things like that. I don't use a time out unless he breaks a set rule.
Also, if your daughter is whining and wanting you, give her some love and attention. I found with my son that giving the attention he asks for works better than not doing so. If I respond when he wants me, he seems to ask for me less, and he is also happy, so I'm not dealing with a tantrum. Sometimes you really can't give the attention and they will get mad, but you can only do what you can do, so if they are mad, oh well.
Also, when my son is getting upset/tantrum, I try to see things from his point of view and talk to him as though I am thinking on his level. Ex: he is mad because he can't have ice cream, I tell him I understand and I want to eat ice cream too, then I explain that Ice Cream is a treat and we need to eat a healthy meal before we have a treat...something like that. This doesn't always work, but usually.
Two is a really hard age. Just try to be as patient as possible...not easy, but you will get through it. And some days are much harder than others. You just have to figure out what your daughter responds best to and handle her in that way...you'll be just fine! Best wishes.