Key derivation design to avoid key leaks
I finally found out what you're asking for:

A specific (working?) related-key attack on AES!

For this answer I changed the notation a bit:


AES-DEC(K,P) got converted to $D_K(P)$
derived_key_X got converted to $DK_X$
seed (which is known) got converted to $S_K$
chosen_seed got converted to $S_C$
temp_key got converted to $K_T$


Now the answer:

AES by itself is immune to related key attacks to a great extent (there are some attacks but I think they require at least four related keys and I'd doubt the relations would be that complex).

So for an attacker to uncover $DK_1=D_K(S_K)$ he'd need to know $K$. There's no other way in doing this.
Now you're asking if knowing $DK_2=D_{D_K(S_C)}(S_K)$ does help. Let's de-construct this. An attacker can choose $S_C$ to be decrypted to $K_T=D_K(S_C)$, in order to learn $K_T$ he'd need to get K which is infeasible for AES. Now as the attacker has no chance to know $K_T$ there's the question left if $DK_2=D_{K_T}(S_K)$ does help him anyhow. He can't deduce $K_T$ from this equation as this would be a known-plaintext attack, which is infeasible on AES. The final question is if there're some strange relationships that may help the attacker in uncovering $K$ and hence $DK_1$. 

No, he'd be (maybe) able to brute-force by trying out every possible $S_C$ until $K_T=D_K(S_C)=K$ which is extremely unlikely, as he could as well just brute force the normal key as he has no control over the value of $K_T$.

I hope this answers your question.