Yup, not much you can do about the age of aircraft, it just depends on how much love a school is prepared to give them as to their appearance.
A usual question you would get asked doing trail flights was "How old is this rustbucket?" at which point you would reply "Oh, not that old" whilst knowing that it was older than yourself and the punter combined... Anyway.
It is important in your training to get continuity. It ensures that your standards are defined and not changed every lesson. It also allows the instructor to identify your weak areas and focus on methods to help.
As said above, try and book your favourite instructor a few weeks in advance when the bookings are still light. If you say to an instructor that you really like their style and would like to continue training with them, they are usually so chuffed with the glowing recommendation that they will make sure that they get to train you the next time, and the next.
However, if you're school is just messing you around then I would suggest voting with your feet. Go in and demand to speak to the CFI, explain your reasons and if still not satisfied, ask for your training records and enrol in another school.