You said the place will be closed by 10pm, so the floodlights will be off by then - I don't see that as seriously impacting you.
By all means lodge an objection to the planning application, but surely it's a GOOD thing to be providing local sports facilities and a place for valuable organisations like the Air Cadets to do their thing?
I get the impression that it's the development which has already taken place which you're unhappy with rather than the current proposal to add a small car park. Well the leisure centre IS there, and it isn't likely to be going anywhere.
Did you object to the plans to build the sports hall and pitches when the application for them was submitted?