We are discussing teens and public schools. Everything you said after that point is irrelevant to the conversation.
Your link is titled "Landmark Supreme Court Decisions About Teens," and all of those cases involve minors. You get thread grades of D- in reading comprehension, F in Constitutional Law, and F in Oklahoma Criminal Procedure.
As far as the K9 thing goes, in the US legal system, if a drug dog alerts on your car, that can constitute probable cause to allow a search or impoundment of the vehicle under the motor vehicle exigency exception to the Constitution. However, mere refusal of consent for a search, or any other assertion of a person's Constitutionally-protected rights, can never be the basis for probable cause for a search or seizure, as some in this thread are saying.
For an adult who is not a student at an elementary or secondary school, both of these things are true whether your vehicle is on the grounds of an educational institution (no matter what kind) or not.
If some blowhard State employee threatens to have you arrested for refusing consent to search, feel free to tell him to get bent.
Oh, and I wish I was kidding about the "exception to the Constitution" thing. You can thank the War on Some Drugs for that.
I agree with Dutch's sentiment... the clearest solution to the kind of problems posed by the OP is to not put your children in the hands of the State in the first place. I know I sure as hell never will. Market alternatives are getting better and better, especially with online based learning.