What you propose is indeed possible. How difficult it is, depends on what wiring is currently in place.
You should start by connecting all the bare/green grounding conductors in the switch box together, including a pigtail to both switches. Other than that, it sounds like the wiring in the switch box is good to go.
If you want to control the fan with a wall fan control, you can install that in place of the fan toggle switch.
In the ceiling box, you'll likely find the 12/3 cable from the switch box. If the existing fixture uses a remote module, you'll likely find that either the black or red wire from the 12/3 cable is simply capped off. You'll see the black/red, white and ground wire connect to the remote module. The remote module should connect to the fixture with a black, blue, white, and bare/green wire.
If you want to remove the remote module, you should disconnect it from all the wiring. Once disconnected, you can remove the module, or cap off all the wires and leave the module in place.
To control the fan using only the wall switches.
- Connect the white wire from the ceiling to the white wire from the fixture.
- Connect the bare/green wire from the ceiling to the bare/green wire from the fixture. If the box is metal, include a pigtail to the box.
- Connect the red wire from the ceiling to the blue wire from the fixture.
- Connect the black wire from the ceiling to the black wire from the fixture.
Now the switch connected to the red wire, should turn the light on/off. The switch connected to the black wire, should turn the fan on/off (and optionally adjust the speed).
You'd need to replace the switch with a remote controlled switch. Since you currently have two outputs, you'd need to find one that has two outputs - I believe they sell one which has a button for the fan and another for the light. Regardless, they'd still have to be separate.
Also, getting this to work would require no modification to the fan itself or the wiring at it. Everything would be changed at the switches.
If you can't find a remote switch module that allows two outputs, then you'd have to leave one currently as is and only control the other.
Best Answer
You can't... Well, you can't use separate switches to control the fan and light, and also use the remote. So you'll have to decide if you want to use two wall switches, or the remote.
The reason that there's only three wires coming out of the fan unit, is because you're only supplying power to the remote module. The remote module then controls the fan and light, depending on what buttons are pressed on the remote control. If you pull out the remote module, you'll find four wires going from it to the fan unit. One wire for neutral, one for ground, one for the lights, and one for the fan.
If you just want to use the remote control.
If you want to use two wall switches
If you want to use the remote for the light or fan, and a wall switch for the other. That can also be accomplished, but I'm not going to cover it here.