"Yo habría tenido que vivir con mi hermana."
Traducción:I would have had to live with my sister.
Supongo que te refieres, "I would have had living with my sister?"
No, no es correcta. Se tiene que utilizar el infinitivo si no hay objeto directo.
Se podría decir, "I would have had my dog live with my sister if my girlfriend was allergic to him" o "They would have had us living on the street if they had their way."
leaving = partido, ida, abandono, (figurado) deserción
living = vivo, viviente, trabajo