Just out of curiosity, what is the first 2 doing in “2(2+2)”…? What are you doing with it? Possibly multiplying it with something else?

Distributing it, as per The Distributive Law. Even Khan Academy makes sure to not call it "multiplication", because that refers literally to multiplication signs., which, as I said, there aren't any in this expression - only brackets and division (and addition within the brackets).

I feel bad for your students

My students are doing well thanks.

I doubt anyone is going to accept links to your blog as proof that you are correct

You mean the blog that has Maths text book references, historical Maths documents, and proofs? You know proofs are always true, right? But thanks for the ad hominem anyway, instead of any actual proof or evidence to support your own claims.