There is inevitably going to be conflict with toddlers, it's how they are. And its a good thing developmentally too. On the other hand 24/7 conflict is very draining, the ideal is to have some conflict but manage situations carefully so it's not a permanent state of affairs.
If your DD is just two, she's still quite little - am guessing she will not be very verbal yet so you are getting the acting out.
My DS is 2.5 and can talk quite well now, so fewer tantrums. But on the flip side lots of strong expressions of wants and wills! If a toddler digs in their heels it is going to be a very difficult argument to win, you need to distract or remove the emotion about the issue then try again later when everyone has moved on.
The trick is to give in to a sufficient degree so that they are not completely frustrated and fed up about their powerlessness ALL the time. If you can say yes, say yes, even if its a bit inconvenient. Eg my DS has to climb into his carseat by himself. It's annoying to stand and wait but I reason with myself that actually his behaviour overall will be better (and my life easier) if I let him have some freedom.
On the other hand don't let them get away with the biggies (they do need boundaries too as well as freedom to express their own agency). Don't let her be dangerous, rude, antisocial etc. I also have rules about sitting down to eat and drink, not getting too wild in the house, being gentle with (esp. younger) children and that sort of thing.
My son is refusing to get dressed in the morning at the mo. Tricky as I have to get his elder sister (4 nearly 5) to school on time. So I manage this by postponing the conflict - I let him eat his brek in pyjamas and take his clothes downstairs. By the time we have had breakfast he is in a much better mood and we can get dressed quickly.
As your DD gets older you might have more success with "if x, then y" type reasoning. "If you put your shoes on, we can go to the playground/you can have your vitamin sweet/insert whatever bribery you like". The introduction of "y" takes the focus of "x" and they forget to make a scene about it!
My son also responds quite well to the "oh no!" approach. Eg "Oh no! You've haven't put your pants on. You will get a cold bottom, oh no!"
Essentially, you are using your superior cognitive skills to throw more things into the mix than their little minds can cope with at once. That way they forget to strop!
Sometimes though, they just have to put up with doing something they don't want to do. They will be cross. That's life!
Good luck