semantics - Can a conjunction be used to combine multiple meanings?

Years ago, while taking a college linguistics class, I posed this sentence to my professor:

I pushed the chair with my mother and a broom.

Granted, this sentence is ambiguous, and I won’t delve into all the possibilities here. Instead, my question is focusing on the conjunction and as well as the word with.

My intended meaning of this sentence had been that my mother had been sitting in the chair (not that my mother had helped me push the chair) and that I had used a broom to push the chair containing my mother.

My professor claimed that the sentence is syntactically correct, but he wasn’t sure if semantically, a conjunction could be used like this to combine separate meanings like I’m trying to do here.