During the summer months, just put your hair up on a bun, or braid it and bun it! Someone invented fans, so bring one, or plug one in. I've seen older men in their 80's, fanning themselves indoors, or walking on the streets, or bring it with them in their walkers.
The answer for you is: It is YOUR hair. She can make suggestions (like I do to my husband when after he retired, to start letting his hair longer). Cut it when you feel READY, and not when she wants you to.