I advise you to drop off at T1 and then return the car.
Any wheelchair assistance must be requested by the airline. NCE has a very good and free wheelchair service.

I am quite familiar with Nice airport and just returned from LHR at T1.
P2 parking is really near T1 (P1 does not exist anymore and has become G1). You could use the "Depose Minute" (Kiss and Fly) area which is also close to T1. Just cross the tram road. It is free, but would charge if you stay 30 min. There are often arriving pax with trolleys, and a trolley station. Frankly it is very close to terminal and convenient. But entails a short walk in the terminal to get to the check-in counters. G1 would be best but might be expensive. You can see a map and rates in this link. Best would be to book online on that link.
https://www.nice.aeroport.fr/en/services/parking

Another map.