I don't think you're missing anything, it's just flat not coded to let this happen. I had two detectives, and once the first went to work I didn't get the option on the second. He was even going to miss work, doing gardening at work, because he wouldn't go in autonomously. The question you are asked is the trigger to start work and you're only asked for the first. When I sent #2 to work, I had to go back to the first and couldn't see the other guy anywhere on the lot. It's like he works at entirely different police station. Too bad! I guess marrying a co-worker you could easily find yourself in this situation, and the game might not even treat their employment correctly.
I am not sure how it works with two in different careers, but suspect there could be bugginess
I think I need to see if this is reported on the EA Answers Bug HQ.