Wire Ceiling fan with two switched hots and ground but no common wire
First order of business: fix the bootleg job

The original installer of the fan couldn't be arsed to put a /3 cable in, so they used the two insulated wires as hot and bootlegged neutral off of ground in the fan box.  Your first order of business with this project is to untangle the work of said dimwit, and that's pretty simple, as you figured out already:


Take the fan-half of the switch out of service by disconnecting it and removing the pigtail that went there
Take the black tape off the white wire at the switch end and bundle it in with the rest of the neutrals in the box
And, take the black tape off the white wire at the fan end and move the fan's neutral from the ground bundle to it


If you're content with using the remote as a (loseable) pullchain, this is sufficient, with everything on a single 3-way switch as a result of this setup.  If you want a better integrated system though, with wallbox controls and a remote that work together in harmony, then read on: there are two ways to skin this cat, each with different trade-offs.  They also require your fan to be compatible with third party controls -- some cheaper fans use an integrated remote system that renders them incompatible with wallbox fan controllers, unfortunately.

If you don't mind "point and shoot"

If you like an integrated, fully-supported system, but don't mind "point and shoot" operation, then I would look at the Lutron Maestro IR MIR-LFQMT family of combination dimmer/fan controllers.  These, as the name implies, use an IR remote control, similar in operating mechanism to a TV remote, to provide remote control functionality.  As a result, you have to point the remote at the master wallbox control to use it, which may or may not be an issue, depending on room layout.  However, in exchange for this, you get "out of the box" operation, with no configuration settings and minimal setup required.

In your case:


The master and accessory wallbox controllers can go at either position, replacing the existing fan switches -- common wire (hot or switched) to black, traveler wires to brass, and a ground pigtail to the green screw.
And the canopy module wires just like a normal fan remote receiver does


Once you turn the breaker back on, you will need to perform a brief setup procedure in order to establish communications between the master controller and the canopy module.  From there, you can enjoy your fan!

If you want more flexibility

If "point and shoot" remote operation is an unacceptable constraint, it is possible to build out a system that provides both RF-remote and wallbox control, but it requires some configuration work, and is a bit more expensive than the Lutron package.

You'll need for this:


An Insteon FanLinc fan/light canopy module
Two Insteon KeypadLinc modules (6 or 8 button, your choice)
An Insteon remote control keypad
And fan button sets for each (if you wish)


The FanLinc gets wired up at the canopy, just like any other fan remote receiver module.  The KeypadLink modules are both wired up as secondaries, with their line-hot terminal connected to the junction of the common (hot) and black traveler wires, the red traveler wire capped off at each end, their neutrals connected to the neutral bundles in each box, and their grounds tied into the ground bundles in each box.  Finally, the remote control keypad needs no wiring, just a good charge before you go in and start setting up the Insteon system to provide your desired controls.