Don’t depend on your school teachers for building your concepts as the level of senior secondary education is below par with the level of medical and engineering entrances.
If possible, take admission in a school where attendance is not compulsory because more often than not, you end up wasting your entire day at school. There has been a mushrooming of such schools in recent times. Such schools are knows as dummy schools. You dont have to go to school at all. They will take care of your internal marks and practicals. Its not completely legal, but all know it happens. Go for a dummy school only when you have joined a coaching institution otherwise not.
Preparing for medical and engineering entrance itself takes care of your school exams. English and optional subject can be handled easily by your own. Lot of material is available online for free. If uou cant manage those subjects by your own then consider attending classes for those subjects.
Prefer CBSE board for XI & XII as the JEE/NEET syllabus is in accordance with CBSE and is NCERT based (NCERT biology , chemistry and physics). If your school is affiliated to some other board, then you should not forget to read NCERT books.
Do not overburden yourself with hectic schedule of both school and coaching on the same day. Self – study is extremely important. Never ignore it.
So a better idea would be school on weekdays and coaching on weekends.
Bunking classes is common in schools. Others do it for fun. You do it for self-study. Practice questions in free period. Do daily assignments of coaching in school time. And if you have to sit through the class then better pay attention to the teacher than wasting your time.