句子's grammar

"that is" (or, "that is to say") is an idiomatic expression used (1) to say what something means or (2) to give more information.

(1) there is no need to put a comma after "is" when explaining "the school swot":

Many people associate thick-rimmed lenses with the school swot, that is someone who spent too much time on books.

(2) when giving more information to the main clause, a comma is required to separate "that is" from the additional information, which could be a sentence or its reduction.

e.g. We'll meet you in a week, that is, on March 30.
(= We'll meet in a week, that is, we'll meet you on March 30.)

e.g. Some poems are mnemonics, that is, they are designed to help you remember something. (Oxford dictionary)


Therefore, your sentence is also correct in grammar, but sentence (1) (without ",with") is more direct and hence better.

---Grammar in the sentence---------
"with" is a preposition.
For the special uses of associate with the school-------we've associate with something/somebody is in the phrase verb at the word(associate)
Hence we've associate with the school;
-------------------associate with someone who-------
Hence the second "with" means because of, as a result of;while the first "with" means associate with.