I would be embarrassed but not horrified. Every day there is one child or another at DD's school that doesn't want to pack up his/her lunch and the teachers make them go back and do it before they can leave. My own DD rolled out "NO!" as a (failed) experiment one day - to see what she could get away with. Now, yes, reinforce things like do as you are told at home, but children also have their own minds and if you come across a 3.5 yr old who has never ever ever done anything defiant, I'd be looking for dials and switches.
For the cucumber, teach her at home to leave it on her plate and say, "No, thank you."
We had a teacher, 20+ year veteran, tell us all sorts of things about SD and totally dismiss what WE told HER about SD. She was the "expert". Yeah, she knew a lot but we were experts at SD. So take what the teacher says, think about your home and if you could do something better, but don't be tail tucked between legs about a cucumber.
And if she's smart - use that. Explain things to her in simple terms. My DD responds pretty well if I tell her why, within reason. I think you did the exact right thing to make her leave the elevator. I bet she'll remember that! And when you need her to listen, try getting down on her level and asking for listening ears and then making your request.
Or "DD, how do you feel when people don't say HI? Does it feel nice? No? Then remember that when you don't say hi to other people. It is polite to say hello to your friends." My DD went through a phase where she wouldn't say good bye - because in her mind, if she didn't say it, they couldn't go. Or she'd cry when it was time to leave and I told her that it made her friends feel bad.
We are currently working on DD that this horrible whining noise she makes when things do not go her way is terrible. "DD, you can stop that noise right now or go to your room, but I do not want to hear it." So she has a choice, and neither one continues the annoyance in my presence. Once the noise stops, "DD, please use your words. I am not a mind reader. I cannot figure out from EEEEHHH what it is that you want or need."
Your DD has words. Encourage her to use them instead of throwing things.
And try not to be draconian. Talk to her. Talk WITH her. Teach her what it is that you do want and not just what you don't. "DD, I noticed that you waited for the stroller to get in the elevator. That was the right thing to do. I'm proud of you."
Friend of mine has very verbal, very clear children. She says that sometimes she has to stop and remind herself that her child is only 4 yrs old, even if she sounds older. Figure out what's typical for a 3.5 yr old and go forward. Your child is not a lost cause by any means.