What happens when playing Throne Room / King's Court *twice* with Caravan?
The basic rule is given in the Seaside Rules, pg4

If you play or modify a Duration card with another card, that
other card also stays in your play area until it is no longer doing
anything.

If you have a chain of Throne Rooms or King's Court, you need to retain the cards necessary to correctly process everything on the next turn.
For your examples, discard the initial card (whether Throne Room or King's Court).  The remaining Throne Room is sufficient to indicate that each Caravan needs to be played twice at the beginning of your next turn.
On the next turn, each Caravan would be played twice for a total of +4 cards.
Two more examples should clarify the remaining edge cases here.
Example 1:

Throne Room (1)

Chose Throne Room(2), doubled by (1)

Chose Throne Room(3), doubled by (2)

Chose Caravan(A), doubled by (3)
Chose Caravan(B), doubled by (3)


Chose Throne Room(4), doubled by (2)

Chose Caravan(C), doubled by (4)
Chose Caravan(D), doubled by (4)







In this case, you will retain

All 4 Caravans obviously (ABCD)
Throne Rooms (3) and (4) as they directly modify the Caravans
Throne Room (2) as it will indicate that Throne Rooms (3) and (4) need to be doubled, subsequently doubling the Caravans again.

Throne Room (1) can be discarded as it is has no effect on the Caravans next turn.
Example 2:

Throne Room (1)

Throne Room (2), doubled by (1)

Throne Room (3), doubled by (2)

Caravan (A), doubled by (3)
Caravan (B), doubled by (3)


Caravan (C), doubled by (2)





In this case, all cards will be retained.  Throne Room (1) is needed to indicate that Caravan (C) needs to be doubled next turn.
King's Court will work the same general way, it just makes for even messier examples.
I've distilled this answer from a BoardGameGeek thread where the answers were provided by Donald X. Vaccarino, the designer of Dominion.
He recommends (as do I, for what it's worth) that you use some sort of tree format to help lay everything out as I've done above.  It will help remind you which cards are affecting which in these tricky situations.