Missouri and Illinois CCW in a school parking lot?

Tldr: I have a job where I travel to schools in Missouri as well as Illinois. I am currently in the process of getting a CCW license in Missouri. I really need someone to explain the laws on having a CCW that I keep in my vehicle in a locked box while I go in to work not only in Missouri but also Illinois, I understand that Illinois doesn't honor my permit (when I finally have one) so do you think I should just leave my CCW in Missouri if possible when I go to Illinois or what is the best way to do this. I do have to stay in hotels in Missouri and Illinois on occasion as well so if there's anything specific with staying in hotels please let me know. Just like any person I only have a CCW to protect myself from deadly harm being used against me. Please if you have any information let me know as I am somewhat new to all of this.