I usually let a parent know if I don't want them in the room with me when I am teaching by saying, Your son/daughter is distracted with family in the room with her, I can keep teaching her with this distraction but she will learn more if it is just one on one.
In fact I do have students who's parents sit in on the lesson every time. They want to learn how to play piano as well (because perhaps they had no chance when they where younger and are excited the dream comes true for their children), but they do not ask questions or say a word through the entire lesson, only their children can do that because afterall the lesson is for them. The parents simply sit, observe and write notes down, this is fine. Usually they get the idea I don't want them to distrub the lesson when I do not answer their questions and carrying on with the lesson with their kids. I'll usually put my hand up with a smile, sorta saying wait a minute, I can't talk to two people at once, while I keep giving the lesson to their children. At the end of the lesson I might answer their questions if I have time, otherwise I (if I have no time or the question takes too long to answer) I will let them know that I must get to my next lesson.
You must realise that because you are the teacher conducting the lesson you are in control as to what happens around it, especially the environment you conduct the lesson in. So if you are uncomfortable having people sitting in your home rearrange your home so you will be comfortable! How? That is up to you, put things away, put things out, do whatever that makes you more comfortable having people in there. If there is a psychological social anxiety that troubles you then you shouldn't be teaching from home in the first place. The size of the room has nothing to do with it, unless it is so small that you are indeed like tinned sardines and you can feel them breathing down your neck while you teach!
BTW, don't discuss any changes to your lessons/teaching over the phone, these things must be done in person. I personally feel it is extremely rude to tell people this or that over the phone, you are running a business and should say things which directly relate to your business with your clients face to face. I have lost my temper with students who I have taught for several years who phone me up to say that they quit. I tell them it would be ok if we did lessons over the phone and you lived hours and hours away, but doing it over the phone it is like you are too afraid to stand up and say what you think. It is just immature imo.