The phone and doorbells are interruptions, but parents can be interruptions, too, usually because they want to talk to you about their child while in the studio.
It's ok for parents to take their -own children's- lesson time, but not other students'.
If the parent comes in at the beginning of the lesson to speak to you, take as much time as you think the topic warrants. Be diplomatic. If you do not want to spend the entire lesson on this discussion, say something like: "I need to think about how we can solve this problem. Let me call you in evening."
If you don't want to spend -any- lesson time because you have so much to accomplish that day, I suggest the following: "I think we'll need more than a few minutes to discuss this, and I hate to take that much time from Susie's lesson. May I call you tonight?"
What if the parent wants to talk -after- the lesson, in what is the next student's time? Obviously, you cannot allow this, even for one or two minutes. Try this: "I'd love to talk now, but it's Jason's lesson time now. Would you like to talk about this first thing next week at Susie's lesson? I'd be happy to do that, or you can call me this evening." Smile and look a tad rueful. The parent will get the message.
Don't leave things up in the air but take charge. As the family prepares to leave, say to the parent: "If I don't hear from you before then, I'll be ready to talk with you first thing next week. See you all then!" Turn to Jason: "Ok, Jason, let's start with...."
Sometimes the parent will speak up during the lesson while the student is playing. The parent might:
Asking you to scold the child is a delicate situation. Sidestep by asking the child what she did with the piece during the week and what she might do with it during the coming week.
The last situation is the biggest worry. You may need to discuss this with the parent directly and privately, taking him aside at the end of the lesson (leave time for this!!), while asking the child to pack her materials, select a book from the lending library, etc.
Couch what you want the parent to do as a benefit to the student: "It's confusing to Teri when both of us are telling her what to do. She doesn't know whose advice to follow." The parent usually will make some response. If it sounds like the beginning of an I-know-how-to-do-this-and-you're-not-doing-it-correctly speech, at the parent's first intake breath you say, "I think we need to talk about this when we have plenty of time. Shall I call you tonight?"
When you do chat, listen carefully to all the parent's concerns. Let the parent talk himself out. You take notes and make empathetic sounds to encourage him to continue speaking. Do NOT interrupt with your rebuttal! You want to know exactly what's on the parent's mind before you speak. If he asks for a response midstream, try to get away with a "yes" or "no" or a "We need to discuss that" or (best) a "Please go on."
Generally, just being heard is what the parent wants.
Also consider the parent's points. Are they valid? Are there things you should improve or change? Why doesn't the parent have confidence in your teaching? Are you being too timid in asserting what you want the student to do? What is the parent's musical background?
If you wish, as a gesture of collegiality, implement as many of the parent's suggestions as you feel will benefit the student and are not contrary to your teaching philosophy. You do -not- have to do everything the parent says!! You do -not- have to do anything the parent says!! -You- are the teacher! The parent is paying you for your expertise!
Sometimes the parent's suggestions are either flat-out wrong or are wrong for the child at this stage of musical development. You indicate that you disagree: "I appreciate what you're saying, but I don't think that is what Susie needs at this point. I will bear it in mind for the future, however."
If the parent continues to complain, be obstructive, and obnoxious to you about what you are doing with the child, call the parent that evening and suspend the teaching relationship: "I'm sorry you feel this way about the content of Susie's piano program. Unfortunately, I don't agree with what you wish me to do, so I think it's better that we stop lessons today since it is obvious that you feel what I am doing is not what your child needs."
Naturally, you have kept up with you accounts payable (with all students!) so no money is due you from the family, and you can afford to drop the student right then.
Whether you offer to help find another teacher is up to you.