Be Kind Rewind is not related to the other two quests (collect parts and then kill Bondo) other than them both being in the alternate time.
You unlock Be Kind Rewind each day by killing the Rusty Prince. You don’t have to do the other two at all if you don’t want to (although it can help to have the follower who helps you kill Bondo to also help you kill the Prince). After you kill him, BKR will be offered back in Rustbolt.