To emphasize what Army has told you, many homeowner's are not fully aware of the control that a HOA has over the community. Have you ever read your bylaws and covenant? Have you ever attended a HOA meeting? Depending on the elected Board of Directors, they may or may not have sympathy for your dilemna. They will be in full legal standing to simply say to you, "sell your third car". Their attitude may be, "you should have known of the parking restrictions prior to purchasing your home".
Read your bylaws. THE HOA may have authority to assess a fine against you for disobeying the parking rule. Things could get quite ugly if you don't abide with their demands. The law is on their side, not yours. Your property is bound by the covenant and as owner you are responsible.
Your best bet is to try and be nice and work with them. If this fails, then if you are up to it run for office at the next annual Board Meeting.
Don't even think of parking on the grass or expanding your driveway. You certainly have a bylaw preventlng parking on the grass, and you probably need approval from an architectural committee to change the appearance of your property in any manner.