The phone and doorbells are interruptions, but parents can be interruptions, too, usually because they want to talk to you about their child.
It's ok for parents to take their -own children's- 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. 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" and say you'll call the parent at home in the 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 turn. 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 they prepare to leave: "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...."
If, at the next lesson, the problem seem to be one of those that will take longer than one or two minutes, conclude the conversation as gracefully as you can with the promise to call the parent that evening. Unless you wish to devote the entire time to the parent.
Sometimes the parents speaks 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 first 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 "Please go on" or a "We need to discuss that, yes."
Generally, just being heard is what the parent wants.
Also consider the parent's points. Are they valid? What is the parent's musical background? 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? Do you need more training?
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!!
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 takes you to task over the last statement you might have to pull rank and say, "Well, you -are- paying me to teach her."
If the parent continues to grumble, play your trump card: suspend the relationship on the spot. "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.