How to prove that someone encrypted a specific (large) chunk of data Alice encrypts her data with HER secret key. Then she sends the encrypted data to Bob who should encrypt it with HIS secret key.

Caroline should then eventually get this double encrypted data.
Caroline only wants to receive pseudo-random (looking) data which would only be decryptable for her if Alice and Bob BOTH tell her their secret key. She wants to be able to use this fact in court in case she and [Alice XOR Bob] get accused of deliberately saving and/or distributing intellectual property illegally.
Caroline therefore wants to be sure that Bob really takes the encrypted data of Alice, encrypts it with HIS secret key and then sends it to her.
How can that be achieved?
Alice and Bob are allowed to use different encryption algorithms.

I suppose AES is not suitable for this task.
I hope I was somehow able to express what I want in a comprehensible way.
I know, my English is bad.
I may be interpreting your question incorrectly, but it sounds to me like you are asking if Caroline can prove (in court or whatever) that she can only gain access to some secret $S$ if both Alice and Bob collaborate in revealing it to her.  Unfortunately as you have currently set up the question, I don't think that is possible, because your question establishes that Alice knows the secret $S$ before any encryption is applied (it's "her data", as you put it).  Hence, it is always possible for Alice to simply tell Caroline $S$, regardless of whether Bob collaborates.

But, if we modify the set-up a bit, it is possible to prove what you want.  We need to assume that neither Alice nor Bob knows $S$, and in addition we need a trusted third party and a secret sharing scheme.  Only the trusted third party, Tim, starts off knowing $S$, and he can be trusted to a) not leak any information about $S$ to anyone at any point, and b) to reliably carry out the following three steps:


Tim generates a pad $P$ - a random string of bits equal to the length of $S$.
Tim establishes a secure channel with Alice (using e.g. secure public key exchange and PKI methods to prevent Man In the Middle attacks), and sends her the string $P \oplus S$.
Tim similarly establishes a different secure channel with Bob, and securely sends him $P$.


At this point, Tim has split the secret into two 'shares', and Alice and Bob only know what their own share looks like (i.e. random nonsense).


Alice and Bob then each encrypt their own share using authenticated encryption (e.g. AES-GCM) and their own secret keys.
Alice and Bob now send Caroline the encrypted shares.


This way, no one (aside from Tim) can know what $S$ is unless both Alice and Bob  reveal their shares (e.g. by sharing their keys with Caroline).  Knowing only one share gives you zero information about $S$ (besides the length), and as such if either Bob or Alice don't reveal their share then $S$ is safe.

As to any concerns about ensuring that Alice and Bob do their part (i.e. properly encrypt their shares) and don't simply forward their shares unencrypted to Caroline, I would note that simply forwarding the unencrypted shares to Caroline is equivalent to encrypting the shares but then revealing the keys to her -- so long as either Alice or Bob does their part properly Caroline cannot know $S$. It takes collaborative effort / incompetence by both Alice and Bob for $S$ to be revealed. If we cannot trust that at least one of the two will keep their key secret and properly run their part of the protocol then no scheme will succeed (so my scheme is not unique in that respect). But given my described scheme, one person doing their part properly is sufficient to keep Caroline provably in the dark.