Here's my gut reaction to your post... I know that scolding and being sent to time out is commonplace, but from my experience, those things don't actually teach the child about not hitting. What they do teach the child is about anger and feeling shameful. Maybe I'm an oddball, but when I was a kid and my parents scolded me, it NEVER made me question what I'd done, it just made me feel really embarrassed and then angry at my parents. And time out or being sent to my room - it just made me more mad at my parents. As an aside, I see this a ton with adults on the roads everyday - have you ever seen it where a car will almost run into another car and so that "victim" car honks and instead of the first, negligible car giving a sorry wave, they flip the other car the bird when it was their fault in the first place!! In my opinion, it's always out of embarrassment and I think it's very similar to your situation with scolding your toddler. In situations like this, I think it's your job to not fly off the handle (scolding) even though what your child is doing may be a huge shock (slap across the face at the park) and you may feel like screaming at them. It may take some time, but I think that explaining about why we don't hit and being a good example is a more struggle/tear-free route to go.
Also, I think changing your expectations of your daughter's behavior might help. She is only two. I know that it's not fun to see YOUR child hitting other kids at daycare, but I don't think it's realistic to expect her to completely understand why hitting is disrespectful and can hurt people - she's still so little. Again, I think your best bet is to talk to her about it and not make her feel ashamed or embarrassed. It isn't going to work overnight, but what does? You didn't show your child how to walk and then they picked it up the next day - it takes them time to GET these things and that's our job as parents, to show them - however many times it might take.
And, needless to say, I would never result to spanking, but I understand that you bring it up out of frustration. That is a total mixed message (not to mention, the laziest way to parent). It's okay for you to hit her, but her not to hit you, what?? Again, when my parents spanked me when I was a kid, I never remembered what I had done "wrong" - I just remembered feeling so scared that they could do it again and mad at them for treating me that way. For me, I'd rather my child not do something because I've explained it to them a thousand times rather than because they're scared that I will cause them bodily harm.
Patience, patience and good luck, mama!