Your post resonates very deeply with me, so I will put myself out on a limb and respond in a personal way. It sounds like you, like me, love listening to music, but frustration overwhelms your ability to enjoy creating it yourself. The best thing you can do for your children is to surpass that frustration. I quit playing the piano for many years out of frustration, and I have now spent nearly as many years rebuilding my love of the instrument from the beginning. The rewards are beyond description, and I can see it clearly affecting how I interact with my own students.
There have been 10,000 tiny steps in moving from not playing at all to finding what joy I'm able to find currently, so I cannot describe to you a step-by-step process for learning to fully engage with an instrument, but I can tell you a few things that have proved to be keys (no pun intended) for me. There may be other ways, but this is mine.
1) A long-standing relationship with a psychotherapist. For me, nothing would have been possible without this. It precipiated my return to the piano in the first place and lead in both direct and indirect ways to the other "pillars" I'll describe.
2) Yoga/pilates/various body-work forms. These practices continue to provide me with invaluable physical self-awareness and freed me from limitations in my physical approach to the piano that I didn't realize I had and that no piano teacher could have discovered. (Of critical importance was a massage technique called SOMA, but I do not know that it is available outside of Seattle. It is, however, closely related to Rolfing, which I believe is available worldwide. I do not have any experience with the latter. I also had an extraordinary one-time experience with Alexander Technique based upon which I'm comfortable recommending it.)
3) Finding a piano teacher I liked who was willing to work with me as though I was five years old, playing piano for the first time.
These are far from the only things I've done--some helpful, some not--but to the degree that I've come to shed my old frustrations, these three things have been of inestimable value.
I just thought of two other important pieces. Again, there may be other possibilities, but for me they've been essential. These are "rules" that resonated with me. I imposed them on myself but judge their "correctness" by having never had a significant urge to break them.
1) Being good at an instrument causes one to enjoy being good at it, but not necessarily to enjoy music itself. This is not sustainable. However, enjoying music itself can lead to been good at an instrument.
2) I play/practice only when I feel like it, and I stop when it stops feeling good to do. This leads to a lot of frustration over wishing that I wanted to play, but while at first I might go weeks or even months without playing, or I might play only a few notes before giving up, now I find that I have to play regularly or I don't feel right about my day.
