I think that you definitely posed questions that we all ask ourselves. I know that I have (and still do).
You may know that my oldest is experiencing her first year of public school this year. Let's just say that for me it has been a long hard year. My daughter did great. The initial adjustment was difficult for her (what do you mean I don't have time to play?) because between school, piano, and other activities her time was very much not her own. That was new and difficult. She has enjoyed her experience, learned a lot, made friends, and learned that she is glad I'm planning on her homeschooling next year (middle school has never been an option in our family). The strange thing is that even after watching Hannah cry multiple times (she's a perfectionist and tears are a natural part of her coping mechanism), my next daughter wants to have her year at public school. Which I think would have to be this coming up year because I'm not doing the 5th grade adjustment again (apparently the homework load increases between 4th and 5th grades). And yet, I really don't want her to go because I'm tired of doing the public school thing. I want my kids home with me, enjoying our time together. So that is something that I am having to think about right now. I don't think you are wrong to want Miriam to stay home. Families are meant to be together! I never see Hannah anymore. We never have time to do fun things as a family because we don't want to leave her out and she is too busy. I'm glad this was a one year deal for her. Maybe public high school will happen on some level - but it will be completely up to her.
You know the reason I decided to homeschool in the first place was two-fold. First, it was about logistics. There was only one school in our area that was not doing full-day Kindergarten (which I vehemently oppose as developmentally inappropriate for 5 year olds) and I didn't have time to do 20 minutes of driving each way to drop her off and pick her up - especially with a newborn. So we opted to keep her home just for that first year. The second reason was because she and I had had a ROUGH year (the year she was four) and I decided that until our relationship improved, sending her to school would be a bad idea. The way to improve the relationship wasn't to spend less time together, but more. And it worked. We both learned a lot about how to live together. What is it about oldest kids? Anyway, after the first year homeschooling we never looked back because we all loved it.
So about the music thing...that is a TOUGH area for me. If you read the TJED literature, they suggest waiting until the kid is begging for lessons, right? And stopping when it stops being fun. But based on the experiences in my own family, I have a hard time with that.
My mom decided she wanted all five of us to learn to play piano - the ward always needs a pianist! Her system worked great at first. I was too obedient to not take lessons. My next sister just loves music and has a natural gift for it. But trouble started with number 3 and kept going. My third sister refused to take lessons after 2 years. She put up such a fuss about it that my mom finally gave in. And once that precedent was set, it was easy for sisters 4 and 5 to quit, also. However, now that they are all grown, they all regret quitting because who has the time and money for private piano lessons as an adult! (As a side note, all three of those sisters played instruments in band and one is still playing hers with the community band - so they did learn instruments). If they had been pushed to continue over that stalling point, they would know how play! So I don't know what to do there.
My personal plan is to try really hard to make piano lessons something FUN. And to let my kids know that if they want to branch out to another instrument I'm all for it - just master the basics of piano first.
I'm also not starting them at age eight. I'm waiting until at least 9, preferably 10. Hannah started at age 9. She's pretty good and she seemed ready. My next daughter just turned 9 and she is not ready. Maybe next year. I did suggest to her that if she wants to learn another instrument (which she does) she could start learning music on her own with all of our beginner piano books. She's enjoyed that and can now play several beginner songs that she has taught herself. I think that's where the TJED stuff works.
I kind of think that as parents, as long as we are always thinking about things our kids need to learn and how we can improve - we're probably doing okay.
I also decided that I needed to have some ultimate goals; character traits and skills that I expect my children to have before they go off into the world. And once I know those, then I can make sure that our daily activities focus on achieving those. All other things turn into a bonus. I can't do and teach everything. I can't make sure my children are exposed to every good thing. But I can set the stage for a life-long love of learning and experiencing the world.
I could ramble on and on about things. I always think about homeschooling and how I could do it better. At this point I don't wonder if it's right. I think circumstances change (thus we felt that it was good to send Hannah to school for a year), but in general this is a good path for our family.