Since you know it is/would be a boundary crossing; I don't know why you would disrespect your T and go. Whether you know "why" or not is not the issue; you can wonder that on your own, here, with your T, etc. for as long as you wish and get that answer. There is no answer though, no "good" reason to deliberately cross another's boundary other than pure selfishness. It won't hurt your T if you go but it can hurt you badly! Please don't go. I believe deliberate self-indulgence is a form of self injury; it becomes a habit and gets harder and harder to get out of and can harm your chances of good relationships with other people or getting to know yourself (because you'll be in the habit of giving in to yourself so won't do the necessary hard work).

But only you can find "why" you want something because only you can know yourself? One could suggest several reasons that might/might not fit for you (but would/would not fit for me because I'd be able to think of them based on my own reasoning?), but it would all just be "guessing" on another's part.

The range is too broad; you could admire the artist in her father or have had a father who wanted to be an artist or wish your T were an artist or feel like Van Gogh and identify with other artists -- as you see, that all has nothing to do with T! The father daughter relationship you imagine between T and her father might be what you wish was between you and yours, you might be hoping T's father paints about his family so you could learn more about T, like looking at photographs of T over time only better because they would be "originals" and "see" more. You might wish you were part of T's family instead of your own or think looking at the same pictures T looks at will help you see the way she sees. You might just want to go out alone and feel "safer" going somewhere there will be people who know people you "know" and trust.

But "why" you want to go/see doesn't really do anything for you. Only actions, "do". All the rest is just thoughts and possible motivations, sometimes good to know but not an excuse for/against the doing.