Seems to me you have three choices.

1 - Disobey, get fined, hire a lawyer and go to court.

2 - Get together with other like-minded dog owners, each chip in some money, and when you have enough money, hire a lawyer to threaten the HOA with a lawsuit and, perhaps, get the HOA to back off and avoid fines.

3 - Sell your home and buy one that isn't in an HOA.

Ben Franklin didn't realize that he was predicting HOAs when he said:

"He who gives up freedom for security, deserves neither."