I use people's names a lot, and I think it would be a bit unusual if someone never used my name at all, but I find the proposed wording of the response to the mother extremely off-putting. If someone said that to me, my thoughts would be "actually, no, I had no idea that you considered it important for kids to use names a lot, nor do I think it's necessarily my job to be modelling whatever the heck you've decided is 'proper', and thanks for implying that I've been remiss in my duties up til now."
It implies strongly that the mother has been screwing up by not using the teachers name, and furthermore, that she should obviously know better. I can absolutely respect that the teacher may have a valid preference for the mother using her name, but that needs to be expressed the way any other preference is expressed - as a gentle request that doesn't chastise the person.
"Would you mind calling me XXX in front of the children? We're working on blahblahblah habit, and it helps them remember when they see others do it too." <--- This is fine. It expresses a preference, indicates it's asking for a favor, and expresses no judgment about the behavior before the preference was shared.
But I honestly don't know how you ask a person to use your name in private interactions without sounding like a twit. "Would you mind starting your emails and voicemails with my name rather than just diving into the message?" It sounds nitpicky and snowflakey.