I'm going to be very unpopular on this thread, but here goes...
With full support from DH, I made/forced/encouraged/supported/cajoled and paid for both our kids to study the piano.
I made sure they had positive and encouraging teachers at every level, changing if they were not satisfactory or no longer suitable for the child's ability.
I sat silently in on their lessons or stayed in the corridor, taking notes and helicoptering DCs' practice sessions. I was completely on board and committed to them learning the piano. Hence my MN username. 
At the age of 10 DS was told "You have reached the level I hoped for when I dreamed of having a child who could play the piano. Any more is icing on the cake." I stopped helicoptering him because he had gone beyond my ability to judge, and left him in the care of his wonderful piano tutor. In September he has his entrance exam to a Conservatory whose average age of entrants is 22. He's 17. If he gets a place he will be doing Conservatory and the last two years of high school together. Good results are predicted in both.
DD started a year later than DS (at 7) and it has been more of a struggle for her. I would define it as blood sweat and tears but she has made good progress and music is now a part of who she is. If I'd given up on her, she would be the poorer for it. When she goes to Secondary School I will offer her the choice of adding or changing to guitar, violin or clarinet but music is a MUST.
I have a pair of well-rounded, sociable and responsible kids. Piano has taught them the value of perseverance and hard work (other instruments do, too). Without my pushing and DH's support they would not have got as far, but it is something that brings me joy and satisfaction.
To answer the OP, I think you should find an instrument you both agree on and embrace it fully. Your lives and that of your DS will be better for it.