I am right there with you. My youngest is only 2 right now, but my oldest is 4, and the terrible twos for my youngest are coming on full force and bringing back all of those memories of the days when my oldest was this age. I just have to keep reminding myself that, just like I had to with my oldest, I have to set limits, stick with them, and STAY CALM. That's the hard part for me sometimes...I get caught up in the battle with her, and that's the worst thing I can do.
As someone else said, I think it is good to give them 2 choices when possible, but even when I do that, my daughter often wants neither one, just out of stubbornness, not because the two choices are bad. Also, to make matters worse, my youngest just is not much of a talker still, so she just throws a fit (partially out of frustration that she can't/won't tell me what she wants, I'm sure) or she just keeps saying "No." So I just have to say, "okay, those were your choices," and walk away, and usually she then calms down and chooses one...I think they are just always testing us at this age to be sure that we really are going to stick to what we say.
On the fiddle farting, I know exactly what you mean there, too. I do think that the best thing is to tell them they must do it, and then if they don't, like you said, pick them up and make them do it (and if it appears to me to be clearly out of defiance, I also give her a consequence for not obeying). I do think they eventually learn that one way or the other, they are going to have to do it, so they can choose the easy way or the hard way.
So throughout it all, I just have to keep reminding myself, and hopefully this will give you some hope, that if you stick to your rules and expectations of her, eventually they will realize that you are the one in charge. I am so grateful for my oldest who (most of the time...although not this particular morning) is an example to me that the terrible twos do pass, and your kids do learn to obey if you are consistent, even when it seems like it just isn't getting through to them.
Hope that helps. Good luck!