-Apologies for the long answer!-
My main philosophy
For me, I've always found its key to respect your child, treat them as much as possible like an adult and they will come to respect you in return.
The "because I said so" always falls down at some point because at some point they will question why, whether its because they are now older/bigger/'smarter' etc. But "Trust me you need to" makes sense as long as they do in fact trust you.
My General Approach
When you have a disagreement and there is time to break it down I think its important to kneel down (get on their level) and give them the chance to speak, give their reasons and then you can counter them.
With things like going to school, if its a discussion your having the night before you can talk about how adults have to go to work to earn money and children have to go to school to learn and that its important, and that as parents we would get in trouble if you didn't go. Then top it off with, and you have fun don't you? you have friends there don't you? you like your teacher etc. I feel this is important because your not just giving them the rules "the way it is" but positive reasons they will like on a personal level. It is also a great opportunity for them to tell you things you might not know and possibly the real reason they don't want to go such as "X person has been hitting me".
If you do this for the things you can then when there is a rush you can use "You need to trust me" because hopefully they will. I re-iterate often with them "When i am using this voice you need to do what i'm saying because its important. So when it comes to a dangerous scenario or a time sensitive issue, I can use that voice and they know implicitly "you know you need to do what i'm saying now, we can talk about it more later". Tricky part of this, is if you get it working, not to use it simply when its convenient, e.g "tidy your room" (I've made that mistake!). Even if you're sick of re-explaining the reasons why tidying your room is important, if you start overusing the "important voice" they will stop seeing it as important. I feel this fundamentally keeps them safe when out and about. Even for lateness I try and emphasise we are late (which they recognise as a bad thing, for example he knows if we are late for his swimming lesson, he gets less time in the pool, which he loves). But I would be lying if I said i had never used it when I shouldn't lol. No one is perfect, but I do try and talk to them later and apologise for shouting etc and explain how their actions lead to it but that i'm sorry and I love them. Again just trying to treat them with the respect that I would extend to a friend or my partner.
How I would approach your current issue
So in your specific scenario, make time to talk to them in the evening and talk to them,
"Why you [parent] can tell me [child] what I have to do and why I
can't tell you [what to do]?"
I would bring up what she said and answer this with something like
"Sometimes its important that you listen to me, and sometimes its
important that I listen to you. If you have a game that you want me to
play, you want me to listen right? Otherwise i don't know how to play
the game. Its not so much i'm doing what you tell me to do, i'm doing
what I want you to do, because I love you and I want to play games
with you. And if you ask me for something I need to listen right? So
that I can consider it. But I need you to do things for me too, some
of those things you might not think you want to do, but you do need to
do them. You might not want to brush your teeth but I know that if you
font they will get broken and poorly and you wouldn't like that would
you?" (it might seem like a lot but as long as the examples resonate,
you will be surprised how understanding a young child can be)
You might want to segway this into a discussion about leaving for school or address it on a different day. Personally I would probably try to do it on a separate day. You could try something like what I had above with your own personal points try and add personal points like:
" you have been not wanting to go to preschool lately, I know
you would rather stay with me, but I do have to <> because <>
and it is important that you go to school, you get to learn <___>
and you get to see your friends:
Then you can point out that they wouldn't want to stop going completely because they would miss out on those things they like. As for lateness this is often harder, mine used to have breakfast at nursery that they would miss if we were late, sometimes they only thing you can do is explain why being late is bad for you and how that impacts things (e.g. more money = more fun things)
The important point is about the listening, i might say something like:
So in the mornings can you listen to me
please, I want us to start the day well and have a nice goodbye, that
would be a nice way to start right? So if i'm ___ then I need you
to listen to me right away, not because i'm telling you what to do,
but because I need you to trust me because i'm just tying to make sure
we can be on time and have a good day, if you do have reasons that you
don't want to go, I 100% want to hear them, but sometimes we have to
leave that until later and sometimes you really do need to listen to
me, right away because its important"
You might want to have a separate conversation about safety and when its really REALLY important to listen. I have one particular way of saying "STOP" that i reserve for potentially dangerous scenarios and they know they absolutely have to freeze.
Other things we mix in
We use 1, 2, 3 whenever we can/remember its a great way of showing things are getting serious without raising your voice (trust me, that still happens, but it helps us do it less), it's good for time sensitive issues too :) "put on your wellies", "no", "sorry, im going to start counting, we need to go", "no", "1"....
We also had a system for a while of green tokens and red tokens, so they knew a 3 was going to be a red token (if they did nice things or even just went to school well they might get a green). Then we translated those into consequences, e.g if they have more green tokens then red at the end of the week we watch a film at the weekend. This can work really well, but lately we have phased out the tokens because they were starting to say "will i get a green token for this" :p (kids work out how to exploit systems fast! :p).
There is no silver bullet and you will have to have this kind of conversation a lot if you want to stick with this idea as apposed to "because i said so" and you might have to mix up your consequences. But personally I think its worth it, no ones perfect and you will slip up and end up feeling like you were a shitty parent for a few weeks sometimes but to be honest I try and let my kids know that too, as long as you remind them you love them and all that jazz kids are pretty accepting of your flaws and I prefer that kind of relationship with my kids to a "i'm right your wrong" relationship, I'm sure its probably harder, but most things worth doing are.
Good luck, you will figure out your own path i'm sure :)