First off, I agree with arved to some extent: once in preschool, let the preschool teachers handle things - if they're willing to. The dropoff exchange is a tricky thing though, and sometimes the teachers will prefer you to make sure she is (somewhere/doing something specific) when you drop off. Most I've met are happy to help manage it, though; but talk to them and find out what their expectations are.
Second, some specific pointers about how you handled this.
I told her, no one is there yet, just sit with your friends and you can go when it's time.
This is a good start. Think about this from her point of view: you're asking her to do something she apparently doesn't want to. Explaining why she should do that - or gaining her buy-in - is important to getting her to do it. The reason is almost exactly what you said above: because that's what everyone else is doing (and what they're expected to do). I would expand on this, and particularly if she's smart, she may well be able to understand why she should do it. My almost-four year old can. He doesn't always want to, but he can understand, and will listen usually when he does.
She completely shuts down, which is her way of giving me a hard time.
Your daughter almost certainly does not want to "give you a hard time". What she does want, though, is to gain some control over the situation, and to express her feelings. Do you object when she "talks back"? She likely doesn't feel like she has a way to express herself and have some control over the situation, so she shuts up.
I take her out into the hallway and ask "am i not your dad?" she says "yes", then I ask "you don't listen to your dad anymore".
Not entirely sure where you're going with this. The latter - "you don't listen anymore" - seems counterproductive, and undoubtedly is an exaggeration. (My almost four year old, yesterday: "You never take me to ice cream anymore".) She's four years old, so for sure she's not going to listen to you as much as when she was one or two: she has a brain, and wants, needs, desires, and is learning how to satisfy those on her own rather than through you.
One good rule in parenting: it's fine to express frustration to your children, but do it in the right way. Be specific, be timely. Your child isn't of an age to have a concept of "across time". Tell her about this frustration, not all of your frustrations - tell your wife or your friends about those. For example:
It makes me frustrated when you didn't listen when I ask you to sit down at the table. I want to drop you off and follow the instructions your teachers gave me, and then be able to go to work on time, so when you won't do what we've been asked to do and make dropoff take a lot longer, I'm late to work. That makes me sad.
And then include something actionable.
Please follow your teachers' instructions and sit at the table with the other kids. It's okay if you're not hungry, but your teachers need you to sit with the other kids so they can watch everyone.
I tell her "then no surprises (treat/toy randomly given once in a blue moon) when you get out of school". She responds with a whiny "yes (like come on man)".
She's not old enough yet for a promise of something later to have a huge affect on what she does now. Add in the randomly once in a blue moon part, and you don't have nearly enough of a tie between cause and effect for this to have any value. People behave well when rewards have a clear, direct tie to actions - no randomness, every time gives the reward, and close in time (reward given within a few minutes or less of the action). If you give, or don't give, her the reward later on, since it's random she won't know why she didn't receive it - did she behave well, and just randomly didn't "win" today, or did she behave badly? And since it's hours later, she won't remember it anyway.
What can work in this regard is a regular minor reward based on whole-day performance that is coordinated with the teachers. "Every day, if you get a clean sheet, we can go get a fruit after preschool." The teachers keep track of her behavior, and if it's clean, she gets the fruit - and is reminded through the day of the reward. But all of this is needed - not just one thing early in the day.
What you've got is a "strong-willed child". I put that in "quotes" because it's a bit of a misnomer - most things that are recommended with strong-willed children are good for all children, and all children have elements of strong-willed children in them. Look up some parenting books on the subject, and find one that works for you.
They've got a few things in common:
Don't shut your child's expression of opinions and emotions down. Encourage appropriate expressions, and teach her how to do so. "Talking back" is one of those things particularly old-school parents fight, but it's not a bad thing as long as it's done in the right way. My son "talks back" all the time, but he does it usually in the right way, and so we get to a better result than if he hadn't talked back.
Find as many ways as possible for your child to have control over her life. Nobody likes other people controlling their every move. Often "strong willed" expressions are simply children wanting control over their life. Find ways to make that happen that don't inconvenience you too much - and keep finding new ones. If she expresses an opinion over something you can reasonably grant, grant it. Have days where you go out and let her pick what you do - and let her make all of the choices that day.
Those two things are pretty much universal in dealing with children like your daughter. Aggressive, controlling parenting styles usually don't work nearly as well. Cooperative styles tend to work much better - and yield better outcomes. Even if your general style is more towards authoritarian, you can find ways to mesh that with a child like this: hard limits which are clear and consistent, and explain why. If she knows where the boundaries are, and knows why, she'll cooperate more.
Go over to Amazon or your preferred book retailer, search "Strong willed children", and look at the selection - find one or two that appeal to you. I won't list them here (because that would be another post the length of this already too long post), but there are plenty of useful ones - if not for following their exact rules, for helping you think about your approach.
