I'm also a music teacher and parent. I actually teach my own kids the piano - I know some shudder at the thought but it seems to work for us.
They're very different though. Older one is not particularly interested and hard to motivate to any serious work. Younger one loves it and happy to do it every spare moment practising.
I actually don't understand why people have such a horror of the idea of "forcing" kids to practise music. We force them to go to school, to do homework, to eat what what we tell them to, to go to bed at a certain time etc. I don't see the difference.
There's a large part of music that is like any other aspect of education: hard graft learning what you need to learn to be able to do it. Because it's a "creative" subject people seem to think this doesn't apply, but it does.
However within this, one can still cooperate with the personality and wants of the child, as with any subject. Eg choosing what instrument to learn, what groups to play in, how much time to spend on composition, jazz etc. One can make a decision from a position of authority that music is an important part of an all-round education, while still making an effort to connect with child regarding how exactly to go about it.
I agree with comments above that a routine helps. I often find that my oldest grumbles and complains about having to go and practise, but within a couple of minutes of having started, he's forgotten about all that and gets quite involved. In fact I can remember being like that myself, and I ended up doing it for a career.
I think music is quite challenging, requiring a lot of attention to the present moment, and the desire not to do it can be more about avoiding that than not actually enjoying it as such. Having a routine time that it just "happens" helps to make that less of an issue, because there's less sense of choice and having to make a conscious decision about it every time.
It also helps if absorption in screen-based media is controlled. We have strict limits on amounts of TV and computer games and when they can be played. At those times of the day when they can't, DC doesn't feel he's missing out on anything by having to do music practice - he'd only be reading a book or whatever otherwise and he has plenty of other time to do that anyway.