There is no easy anwer for this as musicality can take years of experience to develop. It's not that you can't be more musical by a concentrating on sounding better, it's that there are just so many possibilties to explore. I think the most important thing is to listen to LOTS of music. Listen to many different artists playing all different styles and instruments. At some point you will learn what you like your playing to sound like. You can listen to people for advice on what to sound like but as you have already found out, your teacher says one thing and your relative another, they each have their own taste and one isn't necessarly "right". By listening to more music and learning the opinions of respected teachers and listeners, then you will have a better musical vocabulary and will be able to make more informed choices.
In your practice, learn how to play loud and soft, legato and staccato, all in varying degrees. There are infinite variations on this. That is one of the challenges of learning an instrument, it's not just playing the right notes at the right time. It's good that you are at least asking the question on tone, at some point, you will be thinking about it in every single line you play, I think it is the most important thing in music. As you mature as a musician, you will start to be able to make choices as to what sounds good in a certain phrase, that means you will start to develop your own personality. All that being said, different periods of music sometimes have established performance practices that can be a guide, your teacher should be able to help you here. Still, in the end, you are over your lifetime going to continually grow in your musical knowledge. What sounds good to you now may change significantly in ten years.