Welcome to Gaia! ::

When I started band (5th grade) I played flute for 2 years. Then, when I joined Marching Band in 7th grade, my BD "strongly suggested" (her way of saying forced) that I go to alto sax. Then, the next year (8th grade), she told me to go to tenor sax. So I've been playing tenor sax for 3 years(I'm 10th grade now) and at first I couldn't stand it, but it's started to grow on me, but I'd still like to switch to a brass instrument, namely trumpet or trombone. I'm practically already part of the low brass, because my parts are usually the same as the tuba and baritone parts. I'm not sure if I'd be able to do the trombone because of the lack of keys and the fact that it is in bass clef, which I'm really not used to; on the other hand, my trumpet friends have let me try to play their trumpets and I've successfully played the Bb scale so I think I'd be able to do it. But my BD is being rather stubborn when I ask her about switching.

Any tips on what I could say to her to convince her to let me switch? And should I go to trumpet or trombone?

^Sorry, but I have to agree with that comment.

If you can already play the Bb scale on the trumpet, then you should switch to that. I'm not used to bass clef either, but I have to know it since I'm learning the piano d:

Tell your BD that you want to try a brass instrument and that you can play the Bb scale on the trumpet. If she doesn't let you, try learning a bit more of the trumpet on the side and even audition to play it if you have to.

For the trumpet, you have to learn...
-Bb scale
-A scale
-C scale
-F scale
-"warm ups"
-your music pieces

Once you learn all four scales and a little bit of music, you should make it as a trumpet player ^-^

It's great that you play so many instruments, it truly is, but I think it would be a good idea to stay a tenor sax player for at least a little longer and practice trumpet/low brass on the side. If you keep switching, you're not really going to excel in any of them. If you discover while practicing the trumpet or a low brass instrument that you are able to play it better than the tenor, show your director and then get their opinion. They are going to choose what would be more beneficial for the band. I've stayed with the flute for six years, and by doing so I've really improved and become one of the best musicians in my band.