The answer here is not set in stone and has mixed basis in real llife. The first quote is stating that the TIC is in charge of the support agencies and operations, though it does not give an all inclusive list of these. Another thing mentioned is that the operations might trump what else is going on with the ship. This is as true as things that go on with Engineering in support of the warp core. The bottom line is that safety comes first, and I think that is how that rule needs to be applied.
As for who runs the Shuttles, the TIC is the lord of the skies and runs the air (space) traffic control as well as the maintenance of the ships. The CAG shares some of this with the FCO. The FCO worries about the utility craft, like the worker craft and shuttles while the CAG worries more about the fighters and combat. Ultimately, they work hand in hand and both work for the CO. The job is presumed to be too big for one person to stay on top of, so we split the duty. The CAG runs the TIC and the FCO is my person on the Bridge. The FCO deals with craft the way the CTO deals with security officers and Marines. Technically, the FCO and CAG could do each others jobs if they had the experience to manage the reasources.
The trick is sometimes learning how to work well together as a team. In real life, there would be regular meetings where the three of us would sit down and decide who would be in charge of what under certain circumstances and so on. You would work hard on establishing a working relationship and come to understand each other's styles and expectations. It is very hard to convey to people not exposed to military situations what it is like to learn to work together in such a way, but knowing that your own lives and those of the rest of the crew on the ship depend on that relationship is a powerful thing. You may not even like each other, but you need to know you can depend on the person next to you in a crisis situation. For all the faults, the Enterprise TV series at least brought a little more of that back into the mix compared to the other series. We are shone lots of peace and cooperation and exploration in TNG, but there is more military protocol and staying alive that I think would be part of the mix that it showed.
I would suggest that you two discuss this more through e-mails and CC me, so I am in on the conversation. I will be happy to answer any other questions or assit if you need it.
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XO LtCmdr Samantha Waters
Lone Wolf
lonewolfdagaz@hotmail.com