Five minutes out of 30 minute singing lesson

[Croleeen]

My daughter recently started private singing lessons and is also taking part in a musical theatre production with the same teacher. The lessons are $35 for 30 minutes. Today my daughter told me after she arrived she had to sit for 5-7 minutes while the teacher finished up another lesson on Zoom. I called the teacher and said she could have texted me to come back 5 minutes later if it started late, as I feel 30 minutes is already not very long. She brushed it off and said the couple of minutes we spent at the end after I picked her up discussing the upcoming rehearsal schedule (at her instigation) made up for the five minute delay the start.
As a single mum $35 is quite a lot for 30 minutes, AIBU to expect the full 30 minutes is spent actually on teaching?

YABU - arguing over 5 minutes is really petty
YANBU - if you pay for 30 minutes you should get a 30 minute lesson

She should have given her 5 minutes at the end

Texting you - while teaching, you coming and going and coming back again, sounds like a truly massive faff, for the sake of avoiding sitting for five minutes.

Your DC should have had the time at the end. But, you need to see how it plays out over time, there may be a bit of give and take over the weeks. So long as that isn't all one way, you're ok.

You need to form a good relationship with this teacher, not become that parent, who always makes a massive fuss about very little.

If it's a one off, I'd let it go but be careful it doesn't become a habit. One of my dc had a private lesson in a sport and it was supposed to be 45 minutes but sometimes he only got 25 minutes. Dd's driving instructor never gave the full hour either, she would give 45 minutes because she needed time to drive to her next lesson

I was walking the dog near her house so could easily have walked around for another 5 minutes, and told her this is what I plan to do each week.... I do feel like I was a bit petty for bringing it up and am worried now I've soured the relationship (altho I was very civil about it and just said next time text me and I'll come back a bit later).

I am an instrumental music teacher and I always give extra time in this scenario. I would never leave the student short of time, and generally I treat any chat/questions after the lesson as necessary to maintaining a good teacher-parent relationship. As you say, lessons aren't cheap and if it were me I would be annoyed too!

She should have given her the extra 5 mins lesson

Let it go this time. Sticking exactly to the minute in an online lesson is really tricky - parents often want a little chat at the beginning or end, and it may mean a few minutes flexibility. If this happens again, you would be fine to say something.
I agree with not becoming 'that' parent. Word gets around...

Ive just re read your OP. I assumed your DD lesson was also on Zoom.
Apologies - in person is much easier to make up the 5 minutes, and the teacher should have done so.

It's much easier to end a lesson on zoom as you've got a timer on it showing how long you've been teaching. When I'm online teaching, the last 2mins is for wrapping up pupil. If not possible then I'd have given the next pupil full 30mins and run over time by 5mins.
However, as this was a new teacher I wouldn't have jumped in straight away so you were perhaps a little unreasonable in that.

Instrumental lessons are expensive and I do feel as a teacher myself that I want to give a full 30mins of my 100% concentration/time. I've watched plenty of others who don't feel this though!

I changed my driving instructor after the second time during a lesson he asked me to pull into a garage so he could use the toilet. Once I could understand, but twice? It then took ages to pull out of the garage again so I lost more than 5 minutes of the lesson... again, seems petty, but I'm sure they would complain if we paid them 15% less than they asked for!