When the creature dies, two things happen: State Based Actions are checked and Gift of Immortality's ability goes on the stack. When state based actions are checked, Rancor and Gift of Immortality both go to the graveyard because they are not attached to anything (CR 704.5n). This causes Rancor's ability to trigger, so that goes on the stack along with Gift of Immortality's ability, in whatever order you choose.

When Rancor's ability resolves, it returns to your hand. When Gift of Immortality's ability resolves, it returns the creature to the battlefield and creates a delayed triggered ability, which puts Gift of Immortality back on the battlefield, attached to the creature at the beginning of the next end step.

Angelic Destiny's ability works the same way Rancor's does, so it would also return to your hand.

After a creature dies, but before triggered abilities are placed on the stack, State Based Actions are performed. The SBAs will cause both Rancor and Gift of Immortality to go the graveyard because they are not attached to anything [CR 704.5n].

Then, it's time to place on the stack the abilities that have triggered. Gift of Immortality's ability and Rancor's ability are placed on the stack in whatever order you choose.

When Rancor's ability resolves, it returns to your hand. When Gift of Immortality's ability resolves, it returns the creature to the battlefield and creates a delayed triggered ability, which puts Gift of Immortality back on the battlefield, attached to the creature at the beginning of the next end step.

Angelic Destiny's ability works the same way Rancor's does, so it would also return to your hand.

When the creature dies, two things happen: Gift of Immortality's triggered ability triggers, and State Based Actions are checked. The first event just puts the ability on the stack, so we'll come back to that later. When state based actions are checked, Rancor and Gift of Immortality both go to the graveyard because they are not attached to anything (CR 704.5n). This causes Rancor's ability to trigger, so that goes on the stack.

Then Rancor's ability resolves, and it returns to your hand. After that, Gift of Immortality's ability resolves which causes the creature to return to the battlefield and creates a delayed triggered ability, which puts Gift of Immortality back on the battlefield, attached to the creature at the beginning of the next end step.

Angelic Destiny's ability works the same way Rancor's does, so it would also return to your hand.

When the creature dies, two things happen: State Based Actions are checked and Gift of Immortality's ability goes on the stack. When state based actions are checked, Rancor and Gift of Immortality both go to the graveyard because they are not attached to anything (CR 704.5n). This causes Rancor's ability to trigger, so that goes on the stack along with Gift of Immortality's ability, in whatever order you choose.

When Rancor's ability resolves, it returns to your hand. When Gift of Immortality's ability resolves, it returns the creature to the battlefield and creates a delayed triggered ability, which puts Gift of Immortality back on the battlefield, attached to the creature at the beginning of the next end step.

Angelic Destiny's ability works the same way Rancor's does, so it would also return to your hand.