Hostile Waters: Antaeus Rising was RTS+Vehicle shooter, very close to what you describe. It is the best game I have played from Gog.com, but is currently removed from their catalog. You should try it if you have the opportunity, but even if not, check out Making of Hostile Waters [http://www.rockpapershotgun.com/2007/12/07/making-of-hostile-waters/] at Rock, Paper, Shotgun.
The player controls a carrier and commands a crew of up to 8, at any time any vehicle can be controlled directly, also at any time the action can be paused to get a feel for the current situation, and any order you would give through the pause screen can also be given directly. Key for this to work was the pause screen and keeping the direct control mode fun (however, there is only one part where you are forced to take control). This isn't a balanced RTS though, the player has finite units that must be purchased with scavanged energy, and the AI opponent has endless waves of slightly weaker units.
Not included is multi-player, there are rumors that a patch was intended to add multi-player, but in reality that patch was never completed.
EDIT: Looks like you can get physical copies from Amazon.com and surely other places, costs about $5 + shipping. I do not advocate piracy, and there is simply no excuse in this case.
EDIT the second to avoid a double post: Also consider X-Com. It is not a FPS, it is a strategy/tactics hybrid that uses a worldwide base management game to frame kill-all-aliens levels. It serves an example of how to have the two modes interact. How you lay out your base will impact how you defend your base. How well you lead the missions impacts what items your scientists can research. Several aspects of it may be informative to your endeavor.
Again, no multi-player.