Mary Joyce told herself she would be kind, just as she always had been. Say enough, but not too much, she reminded herself.

Surely, the members of the Tennessee General Assembly before her would be moved by her testimony at a special session dedicated to public safety.

A moderate conservative herself, she would tell them about the day in March when she dropped off her 9-year-old daughter at the Covenant School, a private Christian school tucked into one of the wealthiest neighborhoods in Nashville. She would remind them how an assailant wielding powerful rifles killed three of her daughter’s third-grade classmates, the head of the school, a beloved custodian and a substitute teacher.

What she wanted now were modest measures that she believed could have prevented the violence and still be accepted by other Republicans.

Ms. Joyce and other Covenant parents felt they stood a better chance than anyone at cutting through the divisions on gun control. Among them were former Republican aides, gun owners and lifelong conservatives who could afford to spend days at the legislature.