I work as a (freelance) instructor in a flying school where we are about 12 flight instructors, and every student flies with everyone of us. The students have a folder where we can exactly see where the students stand, and we give briefings to each other between the instructors. The advantage of this is, that you as a student can learn something from each instructor, and get a fuller picture than when you just learn everything from only one person.
However from what you describe, in your school there is no clear structure. As others already said - change the school, even if it means you have to drive a bit further to another airfield, it will pay out in the end!