So, Fight From a Combat Trained Mount says you have to pass a Survival check as a quick action to be able to have both rider and mount attack in the same round. If you fail you can only make one attack between the mount and rider.
I guess it comes down to if you think "directing a mount in combat" from the description of the combat saddle includes the action Fight from a Combat Trained Mount.
To me fighting from on top of a combat trained mount is included in "directing a mount in combat" since the mechanic is giving it orders to move and attack.
The skill check implies that you need to actively guide the mount in some way. Whereas the mechanic is giving voice commands to the drone which it carries out to the best of its ability without fail.
Not going to cover much else, though - for example, I can't really see a ruling that Spur and Leap are included; it helps that Fight from a Combat Trained Mount has "direct a mount" in its text.