Triangulation with Single Tone FM TX and Three RX using Phase Detection
There are plenty of FM demodulator ICs. Which one you'll need will depend on a number of factors. Use a mono audio demodulator for large distances, use a video demodulator for medium distances, or forgo demodulation entirely (and simply use discrete components) for short distances. For high accuracy long distances, perhaps use some combination.

Example ICs:


Video FM demodulator IC: LA72912V
Audio FM demodulator IC: LA72914V


(Found using a simple Google search: "FM Demodulator ICs".)

Then use an appropriate ADC to get the signal for determining phase. 

As an aside, you might want to use something other than a sinusoidal signal; perhaps a triangle wave or several superimposed waveforms or whatever. 

Very interesting project by the way! I'd be very interested to know what you come up with.

Edit: 

With distances of approximately just one wavelength, that is about as difficult as it could get. My thoughts:


I imagine you will not find an IC that can help you. 
On the one hand, the phase of the FM signal alone will not give you the information needed to ascertain distance greater than one wavelength. On the other hand, you will have trouble modulating a signal with enough bandwidth that will give you the resolution of distances in the order of a few wavelengths. It would be a very specialist IC, and I cannot think off the top of my head what sort of applications such ICs would have. I know little about GPS, but perhaps that's something to explore.