Congratulations! She's reaching a new developmental milestone - she's starting to become an independent thinker - a real human being with ideas and plans and desires! I thought I'd give you a different perspective to think about, seeing the flip side, instead of a "discipline problem". Welcome to the toddler years!
I psyched myself up for the "terrific twos" and tried to accentuate the positive aspects of the toddler behavior. Whenever possible, try to see the world from your child's point of view - empathy leads to (some) understanding. Although I'll warn you toddlers can be mind-bogglingly irrational, and from what I've seen, intelligence seems to make no difference.
In areas like this, you'll start to see stark differences in opinion, and it might seem at first to be a choice of "parent in control" or "child in control" -"disciplined" or "permissive" - "order" or "chaos", but that's not really an accurate view.
Remember "Charlie and the Chocolate Factory" and all those horrid children? No parent wants to raise a "Veruca Salt", "Augustus Gloop" or any of those other nasty personalites. And some people believe that the only way to avoid raising atrocious children like that is to insist on compliance and obendience, always maintaining parental authority, and making sure the big people, well bascially, have all the control. And it can be frustrating for anyone to have someone else always calling all the shots, and to have to always meet someone else's expectations or demands. To always come when called. (Yeah, I know what I'm saying is completely opposite from what everyone else is saying about "this is a battle you have to win every time" and all. After reading Positive Discipline, I've learned how detrimental it can be to allow something to become a power struggle where the only way I can win is for the kid to lose, so I've found ways to gently nudge in my direction rather than get in a tug-of-war. What's the point of being an adult if you can't use your smarts and everything you've learned in your life on the art of persuasion? I don't even hold "consistency" as the gold standard, because every day, EVERY DAY, I think of something I have done as a parent that I know I could have handled better. And I'm not going to do the same thing just in the name of "consistency" if it's not working or I think I've come up with something better. I'm continually adapting and refining, and tailoring it to what is what is not working with my kids.)
You said you want her to respect you and do as you ask. But think about it, YOU won't do everything SHE is surely going to ask you to do, and that has nothing to do with whether or not you are treating HER respectfully. Respect is more about considering the feelings of other people, and taking their wishes into account, treating them with kindness, not doing everything someone says regardless of one's own feelings. This may be a good time to think about how you want to teach respect - it is possible to model it, to treat children respectfully (like allowing them some degree of choice or freedom) and still maintain the expectation that they also treat adults respectfully.
It depresses me sometimes how many parents insist on repect from their children, but don't model it - they don't treat their children with much respect. It ought to go both ways. Keep in mind that they won't really have the ability to truly empathize, to really understand that other people even do have a different point of view until they are older. Try as you might to explain The Golden Rule, it's fairly complex thinking and they probably won't "get it" at two or three.
Now of COURSE it can be a dangerous situation if a child doesn't understand "STOP!" when it's vitally inportant. But I don't believe that the ONLY way they will learn to obey when it is essential is to insist that they obey always, consistently, every time. (I think it was in Dr. Sears' "Discipline" book that he wrote about how his wife had a special voice that she used in such situations, and it sounded so urgent and so different that it immediately got her children's attention. It wasn't even something she planned, she just saw her child heading toward danger and screamed "Stop!" or "No!" and the kids could tell it was different, they were scared and stopped dead in their tracks.)
Sometimes people will suggest discipline techniques that strikes me as overly simplistic - like anytime they talk about "magic words" (like 1,2,3), I'm a bit skeptical. The relationship you have with your child is very complex and I think it's unwise to rely on... well gimmicks. (Imagine being angry at your spouse or a friend and when you try to express yourself, they say "That's one". And if you continue to express your anger, they say "That's two.... That's three. Take a time out." I mean, talk about shutting down any useful communication.)
When my eldest was a toddler I used to think the "Supernanny" Jo Frost had good advice, even bought the book. Then I read an article called "Atrocious Advice From The Supernanny" and thought to myself, "you know, he's got some good points there." That author (Alfie Kohn) got me thinking differently. (You can google for both Jo Frost and that article, which was written by Alfie Kohn.)
If you walk through the bookstores, you'll see a lot of advice on how to get your kids to do what you want, and an awful lot of it has a negative tone to it. (Like "I Refuse to Raise a Brat" "Backtalk" "Don't Have Them If You Won't Raise Them" "Dare To Discipline" - just these titles sound oppressive to me.) I prefer books like "Unconditional Parenting: Moving From Rewards and Punishment to Reason" "Positive Discipline" "How To Behave So Your Preschooler Will Too" "The Happiest Toddler On The Block".
So this is the beginning of a new era - it's the first time you start dealing with child that has independent thoughts. It doesn't HAVE to be confrontational, parent vs. child, "how do I get her to do as I say?". You can work together. You're smart, use persuasion instead of force. You can catch more flies with honey than with vinegar, as the old saying goes. Don't grab her forcefully, if you can pick her up gently. Don't pick her up at all if you can tell her to do something. And don't tell if you can ask her. And don't insist on things when it's not really all that big of a deal. I've seen parents go out of thier way to turn a the most trivial decison into a Lesson in I'm The Mom And What Mom Says Goes. Period. (Sometimes, parents feel pressure to do this because they want to look "in control" around others, and I'm thinking to myself, "Gosh, lady. Take a deep breath - you'll stress yourself out.")
After all, you're raising a human being, one who eventually will need to think for herself and make
her own decisions, and they don't get to practice it if you focus TOO much on compilance and obediance. At the same time, we all know that kids don't always do the right thing, and that there are adults around for a reason. Everyone has to walk that line between treating your child like a dog, expecting them to obey every command, and being such a martyr or pushover that the children have no idea of how to treat people respectfully. When you give them freedom and the ability to make choices, sometimes they will screw things up a bit. But it's also a good way to learn. If you let them make some mistakes, they learn to make better decisions. (Have you ever met one of those kids whose parents make all the decisions for them until they are 18, and suddenly they are out on their own, finally make a few decisions and make some profoundly unwise ones?) Of course, there are many many mistakes you don't want them ever to make and will do everything in your power to control, repectfully or not. (I'm thinking things like driving drunk, playing Russian roulette, trying to beat a train.) Even I can understand that there is a time when it's acceptable to be a dictatorial tyrant.
Your ultimate long-term goal as a parent, unlike most other jobs, is to make yourself obsolete. It was Ben Franklin who said "It is the first responsibility of every citizen to question authority". He didn't say anything about making exceptions for short citizens who refuse to eat their vegetables. The kid's gotta start somewhere.