What is your opinion on the behavior of this sister and her husband regarding the problem of my brother who watches immoral movies, and is this the correct method of Da'wah?

Calling to Allah is not limited to mosque lessons. Rather, the caller should make his voice reach as far as possible. The prophets exerted their utmost in da'wah, like our Prophet Muhammad, peace be upon him, who called people in markets and clubs, sent his messengers, and strove to elevate the word of Allah. Likewise, Noah, peace be upon him, called his people night and day, openly and secretly, depicting his utmost effort in calling them by saying, as narrated in the Quran: "He said, 'My Lord, indeed I invited my people [to truth] night and day. But my invitation increased them not except in flight. And indeed, every time I invited them that You might forgive them, they put their fingers in their ears, covered themselves with their garments, persisted, and were arrogant with [great] arrogance. Then I invited them publicly. Then I announced to them and I secretly advised them secretly.'" As for advising your brother, you can advise him indirectly through tapes and brochures, or directly in a gentle tone, while utilizing the mentioned fatwas.