As per Corporation rules one parking is one car but there are instances that the parking lot is long and can accommodate two cars it is advised you write to the society and indemnify them from misuse of extra space ans then society may reconsider

You have 2 flats in society 

2) you should be allotted 2 parking slots 

3) if number of slots are lower than flats in society it should be done by drawing of lots 

Yes as you are 2 members you can park one car on your mothers name. Nowadays co-operative society has become a goon and they thing they are land lords

1. Since you own two flats there is no hurdle to keep two cars in the society.

2. The claim of the society to consider you to own one flat but 2 fats is wrong and hence it can  not restrain you from parking two cars inside the complex.

3. So you can raise the dispute with the registrar of the society and seek redressal of your grievance.

4. If you get no protection then file writ petition in high court.

Yes you can park another car if your mother doesn't have any car to park in the society for that you can have a letter of permission from your mother to use her Parking spot. 

if your mother is agreeable then you can park

Dear Sir

a) Depending on the number of lawful Parking spaces (under BMC rules) and number of member vehicles, Parking space may be tentatively allotted on yearly Rotation usage system, which depends on cyclic First Apply First Allotment system.

b) More than one parking space may not be allotted to a member IF other members

b) The members DO NOT own the common spaces (Stilt, Open or whatever)

c) Allotment of Parking space is a “Administrative function” and the MC as well as General Body are empowered to allot the parking space to its own Registered members

d) Registered members include family members and associate members

e) Tenant’s are Nominal Members and have no rights of a regular member, which includes having no rights of parking of parking in the CHS premises. However, at the discretion of the MC, parking can be an extended as humanitarian facility to the nominal members.

Under Section 84 of the MOFA Act, Every member who has allotted the stilt or the parking space shall be required to pay the parking charges at such rate as may be decided by the General body of the Society at its meeting, irrespective of the fact whether he actually parks his motor vehicle or not. The Society can recover different rates for different types of vehicles.
The General Body of the Society can definitely fix up the charges for the 2nd and 3rd car etc. Therefore, the member will have to pay the parking charges for a particular month irrespective of the fact that he has parked the vehicle for a few days. Where a member has been allotted more than one stilt parking space, he shall pay parking charges in respect of every such stilt or parking space, as decided by the General Body Meeting.

As long as your mother is not having any car, and she permits you in writing that the parking allotted to her by the RWA be used by you; the AGM should have no problem in this. 

Definitely as mush number of flats own by family shall be count as separate unit, separate parking shall be allot.  For any coercive action, complain to registrar. Your mother will you written permission while CC to management.

If your mother is occupying the flat as a owner, she can very well park the car on her name in the car parking space allotted to her.

The society cannot show discrimination to this effect and refuse her the parking space.

She can take up the matter with the registrar of cooperative societies or even to the consumer forum for relief and remedy.

It is not necessary the car has to be on her name only.