Enc-Mac (AES CTR+CBC) mixing AES-256 and AES-128 and splitting keys
Don't share keys (or derive new keys with a simple method like splitting the original key) for different purposes. If you can't generate truly seperate keys, get a "master key" and derive two keys for encryption and MAC with a strong hash function.

Sharing a key for encryption and authentication with ECBC-MAC is really bad. Splitting the key to generate new ones sounds insecure, but it could also be secure - do you know it? In any case your scheme will break totally if an attacker learn either your encryption or MAC key. That itself is already bad, but with your scheme it's really simple to get the respective other key, compromising both.