Dear Moon,
HOW I can relate to all that you said!!!!
I started playing violin at the tender age of 38 (will be 40 next month). Never learnt an instrument before in my life, did some music theory at age 5 to 7 at school, never revisited it since.
My first teacher don't get me wrong, did teach me a lot of things and got me up to grade 4 (somehow!), and he was a really nice guy, fun to learn with etc BUT as I developed on the violin and the more I discovered (on here and youtube etc) I realised I was not 'learning properly'.
I kept on asking him why we never did scales nor 'exercises' over the 2 years and a bit I've learnt with him, he kept 'fobbing these things off', saying I can learn technique from playing pieces.
I started getting SO frustrated after just 2 years with him that I asked him straight one evening, 'WILL YOU DO SEVCIK EXERCISES WITH ME?'
he refused, kindly and simply refused! My heart 'sunk', I knew it was time to MOVE ON!
and moved on I have!
I started with a new teacher in June this year (or thereabouts), I 'picked him' from amongst others as he sounded like the 'serious teacher' I always wanted.
I always wanted to 'learn properly', just like a child prodigy would learn (with the difference that I will never be a prodigy and will never have 4 hours a day to practice), but nevertheless I wanted to be taught technique properly, even though I would never become a professional, don't know if I am making any sense here.
Not only the new teacher I 'picked' sounded serious on learning properly, he studied himself with great violinists (had Sacha Lasserson as a teacher), so maybe there was a chance he might have some good things to pass on to his students. Ok, studying with famous teachers doesn't make you a good teacher yourself, but there might be a chance that this has helped you if you have it in you to be a good teacher.
Anyway, he puts emphasis on regular daily practice, not so much 'how much' but regular, he insists it has to be half technique and half music, so if I practice 30 minutes 15 on each, I try to practice at least an hour 5 days a week (I work 6 days a week, average of 50hours a week and commute to work too). Indeed my lessons with him (I have one hour once a week with him) are always half technique half music.
He started me on Sevcik op 1 and op3 and Kreutzer n.2, n.4 and he will soon start me on Kreutzer n.1
He has given me a new 'fresh approach' on how to learn music/pieces, the other teacher just 'made me play' and insisted on dynamics, this new teacher helps me to learn by giving me different ways to learn a piece.
For example, I have a string of very fast notes to play in a piece, he has showed to practice this difficult fast piece by applying different bowing variations/different rythms etc and since I have really seen a difference in how I am learning!
I know HE IS THE RIGHT TEACHER! for me anyway.
The sevcik exercises are really helping my intonation and finger placements, only now I realised how 'wrong' I was learning, I was just 'guessing' before, now I know exactly what I am doing and what I am supposed to do!
He makes me work hard and when I think I am just about to start playing something 'reasonably' he pulls it apart again by giving me another way of playing it! hard work, but I can tell it's paying off!
I have realised that my first teacher never 'took me seriously', I think he probably thought to himself:
'she is 40 years old, never will do this seriously/professionally, if I teach her to play some tunes reasonably ok for her friends and family then that will do'!!!
how wrong he was, I may only play to friends and in amateur orchestras in future, but I've always been a person who likes to 'do things properly' and to the best of my abilities and beyond, I like 'pushing myself', I think I made this clear to him many times but he refused to see it my way, it was his way only and I think the relationship has to be 'two-ways'.
Anyway, sorry about the long rant

have let the steam out now!
It sounds like you have found a good teacher too!
we shall both leap forward soon