I absolutely agree. Although they are not music teachers, both my parents are teachers/professors and it has never gone well. There has to be a separation between the parent who raises you and the teachers who want to make you (academically or musically) better.
My mother gave private lessons to a number of my brother’s friends and it always went well, but add one of us children in there and it was a complete mess.
Interestingly, it is the same with relationships : my partner is a martial arts teacher but I simply cannot study in one of his classes, however brief.
The most successful musicians I know did have parents that were into music themselves, but they didn’t play the same instrument. I know of an organ-maker with a violinist son, or a violin teacher with a harpist kid, and the child is thus encouraged to play music but there is no mix-up.