my sister plays with her dogs, for his dogs it would need to be my brother, mi hermano. But then again in context, my sister could be playing with someone else's dogs and if that person were male his dogs would be correct.
'his' es uso para niños y hombres, nunca para niñas y mujeres. Tu habria hablar "My sister plays with her dogs".
Puedes hablar "My brother plays with his dogs". Eso es "Mi hermano juega con sus perros."
Lo siento para mi Español, jajaja.