hi smit,
after seeing ur schedule i got really cofused if u got hardly any time for studying n hw r u managing both at a time.... in these situation, i wud suggest u dat u must hav joined iit coaching only in d weekends...as it is d best option available to a jee aspirant if he has to go school at a regular basis as u can cover d whole thing taught during weekends in d week days n u also can give time to ur school as d recent jee papers  mostly focusses on d need of school education so it wud be better for u to join coaching during weekends as many of my frends from delhi use to hav d same routine .....
but if u r n't able to do den it totally depends on u dat hw r u going to study at d weekends as dis r d two days which u got for studying...so try to utilise des two days properly n i think u can do ur coaching assignments during weekends but it wud be better if u can go thru ur coaching notes on d same day in d night before going to bed...as it is d most important part of ur preparation , u must be clear abt concepts..
Also u can do ur coaching assignments in ur classes at ur school if u think dat dey r not so much important....so in d end i wud say dat u hav to be very efficient in ur approach ..