Honestly, she'll keep doing this because you're letting them. And sadly, I don't recommend a letter to the coach either. Look the coach straight in the eye and say, "I'm paying you for my daughter's lesson, not to confer with other parents. You need to fix that." FGS, don't say "how can we work on this?" YOU are not the problem, the COACH is the problem. And the COACH needs to be politely told she needs to fix HER problem. Do not make it your problem.
Let me give you my example:
My coach (who is wonderful and I respect) had started late with me a couple of times. After the second time I just told her " We're starting late again." (I'm the last student before the zam) and she told me she needed to confer with the mother. I said, "Then you need to build that into her lesson, not use my lesson." It hasn't happened since. See, polite, businesslike, professional. No dithering. No harm no foul.
Skating is a business. You need to be absolutely straightforward and tell the coach politely get her act together.
You should have done this after the second interruption. But since you didn't you've tacitly given them permission to screw you over. And they're doing that. And they will keep doing that until you get some backbone.
Give the coach one warning, and if it happens again, get tough. Deduct the other mom's time off your payment.
And if that doesn't work complain to the skating director and find another coach.
The coach is supposed to be a professional, that means she needs to be able to handle needy parents. Which means it's the coach's job to rebuff the mother.
Skating is a business. The coach is not your friend or your daughter's friend. You are paying her to coach, make sure she does that.
http://icedoesntcare.blogspot.com/2012/05/stuff-i-dont-put-up-with-anymore.html