You should always play musically especially when you are alone in your practice room. This is the place where you can really let yourself go and try things. No one will hear you so go for it! You will be able to play musically in concert only if you practice this way. If you never take any risk in your practice room, will you take some in concert? Most likely not. So don't wait for a miracle; make it happen right now and you'll be able to do in in a performance.
It is not a good idea to practice on worn out chops. You should always plan to take breaks in your practicing sessions especially if you are doing 2-3 hours everyday. First warm up in the morning and let your embouchure rest for 15-20 minutes. Then start working on what you need to prepare for your lessons, rehearsals, concerts etc. Depending on what you play, you'll have to adjust the length of your practicing time. Ideally, you should be doing 30 minutes sessions followed by 30 minutes breaks. You can use that break in a productive way by singing your music or working on your ear training. It's not a waste of time. Of course that depends on how much time you have. Also, low brass players can play longer than horn or trumpet players so it also depends on which instrument you play. The bottom line is don't wait until your chops are dead to stop. If you practice on a worn out embouchure, you will eventually have to force to get the notes out and develop bad habits.
If you plan on increasing your overall practicing time, do it gradually over a few weeks. Suddenly going from one hour a day to three hours will damage your embouchure and you'll have a hard time playing after a few days if the change is to abrupt.
I've seen students going to a band or orchestra camp suddenly playing 6-7 hours per day while their embouchure wasn't used to it. They could barely play after a couple of days. If you find yourself in that situation, remember that the most important is the concert at the end. It is not necessary to play all the notes all the time in all rehearsals. You can always take turns in the section if you have a lot of players. You also don't need to play the loud long notes over and over again. See it as a marathon, the concert being the final sprint.
If I have a big concert to play, I usually take it easy during the dress rehearsal. I avoid playing high, sustained, long notes or repeated notes if they're not too important. No conductor has ever complained about it. They usually understand that you need to save your chops for the show.
To play more musically, you can imagine that the music you play is film music. Create a scene for every phrase you play and try to "accompany" this scene with your instrument. Make a whole story out of one piece and and use it to inspire your playing. Play the story rather than the notes. Of course, if it already is film music you are playing, you should have no problem finding the story!
I am associate principal horn of the Singapore Symphony Orchestra and the author of the progressive methods. I'm happy to share my experience as a horn player and teacher with you.