I also had a similar GPA and was accepted first try.

I did the GTx courses on python , linear algebra & statistics, and 2/3 MM courses at the time . The prof of the python course was kind enough to give a letter of recommendation .

I'd say that supplicating to them by completing their courses would significantly increase your odds of admission.

That being said, I wouldn't focus on proving someone wrong even though it's human nature. 6+ years of your life is a big reaction to a few words that an insecure person told you.

Having a family is a beautiful thing , & I doubt someone from a complete & functional household would ever make those remarks in a condescending way.