Why not increase the lesson to half an hour and tell her that after about a month it would be preferable for you to teach him on his own? Tell her that by age 6 most children have lessons on their own and that it usually facilitates independent learning. If they come by car she could always sit in the car (many of my parents do) - if she comes on foot she can go for a walk unless it's raining. Some of my mums go for a short walk and it really isn't a problem for them.
If he can only concentrate for about 20 minutes (fair enough at this age), how about this: he has a 20 minute lesson with you on his own and she comes back and into the room for the last 10 minutes where you go over what you've taught him so she can help him when he practises?
I've just taken on a 7-year-old girl - after one introductory meeting with the parents present, she had her first proper lesson on her own. After 20 minutes the dad and little sister came back (they'd been for a walk) and the pupil and I then showed the dad (and little sister!) what we'd done so the dad could help with practice.
We've also arranged two half two lessons a week for the first month to get her really well established. This is all a new experiment I'm carrying out for an optimum beginning!
I do know some of the teachers here always have the parent in the room for the first few years - partly to avoid any accusations of abuse and also to help with practice. Different strokes for different folks, I guess.
My mum stayed in the room till I was about 11, took (admittedly very useful) notes and always helped with practice until I was older, but my teacher now tells me it wasn't her who requested it, but my mother! But my mother swears it was the teacher! But as none of the other mothers of my teacher's pupils stayed... oh well, perhaps it was all a big misunderstanding and as neither of them spoke English that well at the time...
I certainly think the mother should go with the teacher and not the other way round. I too find it embarrassing if a parent insists on staying, although the 10 minute pupil/parent/little sister session wasn't embarrassing at all because I felt in control. Perhaps that's the key issue - the teacher needs to feel in control. A parent who insists on being there and then talking into the bargain must make the teacher feel very annoyed and disempowered, so at the very least you must tell the teacher
absolutely no talking is allowed from her side until the end when she can ask questions.
Grrr! Some mothers!
Violinia