I have a fantastic young girl studying piano with me - one of the most naturally gifted students I've had. The mom seems to show an almost unusually high degree of respect for me - they have given me expensive gifts, money on Chinese New Year, recommendations to other parents...etc. The mom eludes to long term plans in studying/staying with me, (asking about me registering for competitions not until late summer or in the fall fall, etc). All seems as good as it gets.

Yet, lately I've noticed some markings in the girl's method books (stickers and pencil marks), along with dates of start/finish, that are NOT mine. At our last lesson the girl looked at her mom and "Mommy, can I say who drew this??" The mom suddenly started to panic, trying to get the girl to change the subject, and then nonchalantly told me that she threw out her back last week so had to "Have a friend come over and help the girl practice"...but to me it seems like there is also a possibility they are hiring a second teacher behind my back.

I'm not sure how to bring this up, or if it's even worth bringing up. I didn't say anything at the lesson. I don't have a problem if there is an occasional "practice coach" that is a genuine family friend or relative, but it seems for now I have way of actually ever getting an honest picture of what is actually going on at home.

Yes sounds like they have a 2nd teacher.

"behind my back" suggests you are not so happy with it? They may feel it and that's why they are trying to hide it?

I'd have a talk with the mother, an the sooner the better. I may say something like, "If you do in fact have another teacher, I don't mind, but I do need to know. We could be working together which would benefit your daughter the most, but we can't if I don't know they exist."

Of course, that is how I feel about it, but if you feel differently, then you should say so as well. Try to be reasonable and non-defensive when you do this though. They have every right to do whatever they wish, but if you have logical reasons for this being a bad idea for the child, then by educating the parent you will be helping the child avoid some issues.

Is the girl playing up to your expectations? Is anything in the way she plays contrary to what you want? In other words, if there is indeed another teacher, is this undermining your work in any way, making her play worse or in a way you don't like?

KS made a good point here. I am fine as long as this student still play very good.

I think this phrase, with its mistaken word usage, says it all.
Allude and elude are quite different verbs. A mom like this - who lies and evades, even in front of her truthful little daughter - would cheese me off.

But let's face it, this is a pushy, nasty parent at work, who doesn't care about you and your relationship to her offspring. My only suggestion is that you get the mom out of your teaching studio during the lessons - where she does not belong.

Whether you are ok with 2 teachers is up to you.

Do we know in fact whether this mother is pushy and nasty in lessons? How does that fit with the description of "unusually high respect" for the teacher?

When I was younger, my mother took me to a piano professor at her friend's urging. The professor was a fantastic teacher (I remember those lessons to this day), and that experience made me look elsewhere for lessons.

So it's not always a bad thing for an occasional coaching from a more qualified teacher. I'm not saying this is what's happening in your case, but I can safely tell you that it does happen, more frequently than what you and I would think.

I think it would be great for advancing students to have someone qualified to help with practice But only if vetted or appointed by the teacher.

I had a family add a teacher without really talking to me first. When I found out I said something like "I appreciate knowing what a student is studying and I'd like to be in communication with the other teacher." They gave me his number, we talked. Turns out the other teacher was a teenage concert pianist, very inspiring to my student, focused on different things in lessons than I do, and while those lessons lasted I think he was helpful. (the student is still studying with me.) I didn't think the family was being deceptive, they just aren't musicians and didn't know the etiquette. Direct questions and clear communication are always a good idea