Are there any issues to doing 2 rounds of AES-128? How is the security compared to AES-256?
Double encryption with 128-bit AES and two different keys does not give 256-bit security. In particular, a classic Meet-in-the-Middle attack applies, with expected cost $2^{128}$ encryptions and $2^{127}$ decryptions. As is, the attack requires ridiculously large amounts of memory, but improvements (using cycle finding with distinguished points) exist that greatly reduce memory requirement. See section 5.3 on MitM in Paul C. van Oorschot and Michael J. Wiener: Parallel Collision Search with Cryptanalytic Applications (in Journal of Cryptology, January 1999, Volume 12, Issue 1).
I find it likely that a system has weaker points than AES-128's key size; systems may be vulnerable against key compromise or side-channel attacks for example.