Family Care Center 387 West IH-10 (Second Floor) Fort Stockton, Texas 79735 The Family Care Center has 2 suites and is located on the first and second floor of the hospital. The Family Care Center is a designated rural healthcare facility with 5 Family Practice Physicians, 1 General Surgeon and with 3 physician assistants and 2 Family Nurse Practitioners and 2-part time Family Nurse Practitioners..