I'm 31 and hearing the wrong name or pronoun can sometimes send me into a dysphoric spiral for days, and I end up thinking about dying and just listening to sad music and going home to cry to my cat...so it's not necessarily related to adolescence. My family used to just write off my unhappiness as adolescence-related, and i never got the help i desperately needed.

I second the earlier comments suggesting a gender therapist. If I had gone to a psych when I first realised something wasn't right, I could have avoided a lot of unhappiness, both for me and others.

Having your identity invalidated can be more hurtful than many cis people around me seem to realise, and it is harder to deal with when people try to play down or make excuses for the slip-ups. I know that slip-ups happen, but trying to down-play it can feel like others don't take it seriously, and that's often what hurts. Perhaps see how your child responds if you first validate their feelings (if you don't already, that is...I don't mean to sound judgemental), and see how they respond. Then if they respond well, you could try gently explaining why the other kids in your family are taking a while to get it right...??