[Theater of Alinda, Ancient Carian City, Turkey, photographed by Ana al'ain, 2009, source: Wikimedia Commons]
Ada was the younger of the two daughters of Hecatomnus of Caria. At some point she married the middle of her three brothers, Idrieus. When their father died, her elder brother and sister Mausolus and Artemisia took the throne. Following Mausolus’ death, Artemisia ruled alone. On Artemisia’s death, Idrieus and Ada succeeded her, ruling together for seven years from 351 to 344. Though Caria was a satrapy or client state* to the Persian Empire, Idrieus and Ada seem not to have been on terribly good terms with the Persians, preferring to maintain close ties with Greece.
Ada should have become the sole ruler when Idrieus died in 344, but her youngest brother Pixodaurus had other plans. He seized power and drove her out of Halicarnassus, Caria’s main city. Ada kept control of Alinda and the surrounding areas and contested her brother’s right to the throne but Pixodaurus had the support of the Persians and she was unable to take power back from him on her own, for all her popularity with the Carian people.
Ada saw her chance in 334 when Alexander the Great brought his army through Caria. She allied herself with him and adopted him as her son. He, in turn, besieged Halicarnassus for her and took the city back. When he moved on, he left her in charge of the last of the fighting, specifically the siege of the acropolis and made her Queen, not just satrap, of Caria. This was a first for Alexander. All of the other rulers he had put in power were Greek, and therefore foreigners. By adopting him, she gained his help, while he gained control of Caria as the legitimate heir of its queen. Ada died eight years later, ruler of Caria in her own right.
*Which it was is rather unclear.
Strabo, Geography 14.2.17 - Perseus
Sears, Mathew. "Alexander and Ada Reconsidered" - Academia.edu
Ada - Livius.org