She hates me! 😔

My 5 year old is very stubborn, today as I was dropping her off at school I told her to get her backpack on and grab her lunchbag like I always say and she saw some little clip thing that had fell off her bag and immediately blamed me right, saying mom you took it off...yatta yatta I told her, no I didnt, and said hurry were pulling up to the school dropping off zone, tell me why every time I dropped her off ( school lady helps her off) she starts acting up?! So she angrily puts her stuff on said says " uuugh, I hate you" before getting off.

Idk what to do I feel like a bad mom maybe I'm to hard on her? But she acts so much older than her age. Her birthday is Dec.16th and she'll be turning 6 this year. She thinks she can do as she pleases with me only not when dad is around tho. I wont lie we've had to spank her a couple of times and when we do I feel so bad like, I will literally cry in my room but I feel like its backfiring because shes so rebellious idk how to speak to her anymore. My husband says we have to be harder on her but I dont think that's the case. She isnt your typical loving sweet little girl. Shes calm and reserved of course she can be sweet and loving which she is but not always. And majority of the time shes complaining about something or her brother, or shes just annoyed and angry. she'll probably act like nothing when I pick her up later on but it really actually hurt me that she said that to me. And I feel like idk how to be a fucking parent! Any advice is helpful. I know not everyone parents the same but I need advice. Tips help!

Thanks