If you want accommodation right in the centre of Granada it is virtually impossible to find a place with parking.
Then if you choose somewhere that does have parking for example Hotel Rallye or Hotel Saray you are not in the best part of town for visiting Granada.

Who would want to come to Granada and then stay on the Camino de Ronda with all the traffic?

In your case you have the additional problem of having someone with a walking problem and Granada is hilly.

Here are some ideas:

The Garnata apartments.
You can drive to the door of these apartments and park in the street for free.
They are not right in the centre but the area is quiet.
They have very easy access to get in and out of Granada.
The 34 bus will go past every hour and this will take you to the Alhambra, Albaicín, Plaza Nueva, Sacromonte, Gran Via etc.
More info
http://granadainfo.com/garnata/

Hotel Guadalupe
You could park in the Alhambra car park which is about 100 metres form the hotel and then commute between Hotel and the rest of Granada on the 32 minibus.
 
Corralon House
This house has a parking space. It is in the Albaicin.
http://granadainfo.com/corralon/index.htm

Clavel Apartment
This house has a parking space. It is in the realejo.
It is not suitable for you because it is for max 3 people.
http://granadainfo.com/clavel


If you park in the Severa Ochoa car park and get a taxi to the accommodation then you don't have to choose your accommodation just from the point of view of parking.
http://granadamap.com/so/index_en.htm