Yesterday I saw an interesting quote from Mark Twain
I do not allow my schooling to interfere with my education.
This may apply to JEE coaching. If you feel, you are not getting adequate inputs, you have to put in your efforts. Finally, you want a seat in the best institute not they.
So do not allow your coaching institute to spoil your education. Depend on them to a large extent, but listen to your judgement regarding your time table.