First, I don't think fidgeting is a symptom of anything other than being 3. It seems to me like it's her version of self soothing. I agree that it's wicked annoying especially when she's in bed with you, but it is most likely a good thing, because you would have to teach her to do it if she wasn't already doing it.
Second, I think that @Joe may be onto something. Try adjusting her bedtime a little later or, earlier. My boy has a harder time drifting off once he's gone into overdrive from being too tired.
Third, have you tried a bath before bed? (Or a shower if you don't have a tub.) Taking a bath about an hour before bed will cause your child's body temp to rise and then drop quickly which triggers the brain to go into sleep mode. I swear by the bath. My kids go directly from the bath to bed, and are asleep within an hour, usually less. A bath can also be a great way to deliver aromatherapy, which I also highly recommend.
Fourth, do not let her sleep with you when she comes in (unless you want her to, which I don't think you do since you are asking for help with it here). Bring her back to bed. Keep doing it. Here's the good news about this though: if you can get her to learn to fall asleep with out you being in the room, this will go away on its own. She is coming in at 2 because she can't fall asleep without you being there.
@balanced mama's question about TV brings me to my fifth suggestion, which is to not allow TV/iPad/computer/video games within 2 hours of bed time. In our house, we try to enforce none after dinner. (We got rid of cable to make TV less enticing.)
Sixth, schedule some physical activity right after lunch or early afternoon at the latest. I think swimming works best at wringing every last drop of energy out of kids, but just do what fits in your lifestyle/routine. Obviously, the more tired they are, the easier they fall asleep. Avoid activity late in the day though, since it will most likely wind her up even more.
Lastly, although I said I don't think the fidgeting is something to worry about, it may be restlessness. If so, a little massage can do wonders to help her little muscles relax. There are videos online you can watch to learn how, or you can just ask your daughter what she would like. One of my kids loves to have his calves rubbed. He would be asleep in minutes after I figured out what he liked/needed.
I can get my three yr old and two yr old down simultaneously in about an hour, including a 20 min bath, teethbrushing, and two books. (Most nights- there are evenings here and there that go awry and we've got kids running around still at 10 pm. We aren't perfect!) It took me about 6 months to get it down to a science though. You are right that it's taking too long, and too much effort, but don't give up! You can get your evening back with a few little routine changes. You really are almost there.