I'de tell you but your offer is too small. Increase it to a medium, and maybe we can talk lol ,jk.
Honestly, it sounds as though key 2 might be faulty or not programmed properly. If key 1 works perfect, and starts your car without any issues, then we know that a: your car is working fine, and b: your key 1 is working fine. So the only thing left is a faulty key 2.
BMW...Now you're playing with power.