Hi,
I agree about the piano/guitar fighting each other but I don't think you need to pick one. I think they just need work.
The guitar is overdriven sounding. Are you compressing it super hard? That's what it sounds like.
Also, it's not a particularly nice sounding guitar. It seems to have a bit of the ol' rattle'n'buzz about it.
I much preferred it when you toned the guitar down into picking.
In fact, I think I'd be inclined to brighten the piano a little bit, keep it as the main instrument, and just play a picked acoustic guitar part throughout.
Nice and gentle though...Mute the piano while you're recording it so you aren't spurred on into really twanging the guitar.
It's hard to tell with the guitar distorting, but I think the whole mix is hitting the limiter kinda hard too, right?
Pull it all back! Your missus' attention isn't going to be drawn by a slightly louder commercial radio station.
You've no one to fight so go for quality.
Real nice though, and nice vocals man.
Glad she likes it.