To not want DD having music lesson with lodger at teacher's house

if The teacher can no longer travel just give notice and find another one. As you have another parent there to supervise during the lesson.

so my assumption is that you are not intending your daughter to be with the teacher unsupervised.
if you are then it’s not really much of a difference if you feel comfortable. But it’s your child safety so you don’t have to be reasonable or compromise if you don’t want to.

i do wonder how likely the teacher is to go back to travelling if she’s managed to get all students to come to her.

I watch a lot of True crime channel stories on YouTube - I would never leave my child alone unsupervised. Literally anything can happen. Trust your instincts

I had a couple of different music teachers when I was younger and found it interesting to be in someone else's home, just to get a little snapshot into how other people in my town lived. My world was pretty small as a child, and it honestly did open up different horizons.

One of my DC goes to his music teacher's house, and prays she'll be running late so he can play with her child-friendly pets while they wait.

I really can't understand why you're uncomfortable with her household. If it's inconvenient for you, then you need to find another teacher.

No, she can't expect the teacher to keep the place open.
While I agree with you that she changed the basis of the agreement with the OP, the OP cannot say the DD will stop the lessons and restart when the weather warms up and expect the slot still to be there.
She can stop the lessons because the arrangements have changed and don't suit. She can stop the lessons and say to the teacher that she would be interested in having lessons again when the teacher can return to home visits. But she can't expect her to keep the place open. The teacher is losing money all the time that slot is not filled and there's no guarantee the OP's DD would start again after the "hiatus".
I'm a music teacher and there is no way I'd keep a place open for anyone like that. I have a waiting list and if someone stops for whatever reason the place goes to someone on the waiting list. I can't afford to be keeping slots open for people who want to have a break. If they want to continue paying then they can keep their slot.

I don't think the teacher is taking the piss by changing the arrangement. It sounds like a genuine medical issue - arthritis and difficulty with mobility when it's cold. It's not someone who just decided they can't be arsed to go out in the cold anymore.
She has a good reason for it, but of course, this does mean that she has changed the arrangement and it doesn't suit OP so OP will either have to make the new arrangement work or find someone else who is willing to come to her home.

I had piano lessons as a child and these were in teacher's home. The only issue is if the child arrived and the previous lesson hadn't finished and they had to wait a minute. That happened a few times.

I do think it's quite a different set up. I would take a break and restart. Zoom wouldn't be a temporary option until the spring would it?

I think the teacher can't understand why you are worried about it, because presumably she wouldn't leave your child's side during the lesson?? I had 30 minute lessons from a cello and a piano teacher once a week for 14 years and could probably count on my fingers the number of times the teachers went to the loo in my lesson. Therefore, the lodger will never have unsupervised contact with your daughter.

That being said, presumably the contract is for the teacher to come to your house, and she is changing this? However much that isn't her fault (health problems are not her fault), if going to her house doesn't work for you, you can always find another teacher.

No, just no

Providing the teacher is with the child at all times during the lesson which tends to be usual for private music lessons/ instrument tuition then it should not be an issue.

I don't think YWBU to try to find a new teacher as the arrangement you particularly chose them for (the fact they came to you) has now stopped. I mean, if there are a plethora of teachers of this instrument in your area who come to your house and that your dc get on with - which seems a BIG 'if').
However, YABU with your concern about the fact your child's teacher has a lodger.
Your child will be there for 1/2 hour, supervised and being taught by the teacher who you trust. What do you think anyone else who happens to live in the house is going to do ? More than likely they won't even see them.

You can't control her changing the venue or who else is in her home, you can only control whether you take your business elsewhere. She's changed her terms, which she's at liberty to do - you can only say yes or no.

I don't think the lodger in themselves would worry me - there is no reason for your daughter even to see them. But as a whole the arrangement sounds like it doesn't work for you.

You can't "expect" a teacher to keep a place open unless you are paying for it. You can ask ... but you and the teacher can both ask for things and can both say No.

What’s the concern here exactly? The lodger doesn’t need to have DBS. Nobody does unless they are working with children unsupervised.
If you find dropping him off inconvenient, that’s another matter and you can find a different teacher. But a lodger is not an inherent. I am not even sure how you found out they are there.

Not my DC, but I am also aware of others. I would also not be that comfortable. Can you find another time where at least you or DH can stay for the lesson. The introduction of an unknown lodger is not ideal.

I wouldn’t be happy about the change either. If you can’t stay then I’d look for another teacher who can come to you.

Yanbu, my dc do music lessons at home. I wouldn't be dropping my child off anywhere with just them and another adult. Clubs are different as there are many people about but this set up wouldn't be ok with me.

Frankly, I think she’s taking the piss to suddenly decide everyone has to come to her. That’s not the basis on which you entered into an agreement with her.

I would say to her that your DD will take a hiatus and restart lessons once the weather warms up. And expect her to keep the place open.

Yanbu.

1. The change in venue for no good reason would be enough to make me change teachers.

1. No, you shouldn't drop your 8-year-old off in a house with a person you know nothing about. I assume the teacher has an up-to-date DBS - does the lodger? What are the safeguarding procedures that the teacher has put in place?

1. None of point 2 would be an issue if the teacher had not changed the venue. Find a new teacher.

I don’t see the lodger as a massive problem per se if you’d originally agreed to go their house as most people do live with others, but I see the main issue is the fact this tutor has changed the terms of your agreement.

She may have (in her eyes) good reasons for it, but it’s quite a significant change to go from travelling to your students house to expecting them to come to yours.

I would cut my losses and bow out now - find someone who will agree to come to yours and make it clear if they change the arrangement to you having to travel to their house you wouldn’t be able to continue.

You’re a paying customer, if you’re not happy - take your money elsewhere.

Any adult living at the address of a childminder needs a DBS check, but I'm not sure how it works for music teachers. If the arrangements don't work out, you might have to think about a new teacher.

I would find a new teacher that can come to my home.

Sorry - but I know too many people that have been abused by music teachers. Be very very cautious.

I don't know what the issue with the lodger is. The teacher will be present all the time. The lodger will most likely be in their room, not hanging around watching music lessons.
I wonder if you are trying to use the lodger thing as a reason to object to having to take the child to the teacher and it's leverage to persuade the teacher to stick to the old arrangement.

If you don't want/aren't able to drive to the teacher's house then tell her that the lessons will have to stop and find another teacher.

Does the teacher's DBS allow for her to see children in her home? From vague recollection, there is a separate part to apply under if you are seeing children in your own home (although it's been a while since I updated mine).

You might feel safer having the lessons at your house, that makes sense. If you trust the teacher though, don't you trust her/ him to keep your child safe?