Fan control & 3-way light switch combo
You'll need to use the correct fan/light control and remote for this
The problem with your proposal is twofold.  First off, most fan/light combination controls are single-pole only units, with no support for multi-way switching whatsoever.  Furthermore, and worse yet, most fan/light combination controls require separate switched-hot wires for the fan and the light, which is something you don't have here.
Fortunately, Lutron still makes a fan/light combination control setup that works for your application, namely the MA-LFQM control/canopy module pair and MA-ALFQ35 remote.  You can put either control at either location, with the black wire landing on the black screw and the white and red wires landing on the brass screws at the small box, and the white and red wires from Cable 1 landing on the brass screws and the red wire from cable 2 landing on the black screw at the large box.  Of course, you'll have to connect the grounds at both locations as well; once you're done with that, you'll need to install the canopy module from the MA-LFQM kit as part of putting the fan up (it's not much different from any other fan remote receiver you'll run into).