The RH96 uses a proprietary connector on one end and a 1/8 " stereo connector on the other. I don't know how you'd connect a serial switch box to that. The RH96 does not use the rear serial port on the X or XT scanners.
If you can use a netbook or laptop to control the scanners could use BCTool+ (or maybe free scan) with either the Uniden USB-1 cable or the supplied serial cable with USB adapters. I know that BCTool+ will control up to four X or XT scanners simultaneously and will display all of the scanners at the same time. Again, I don't know if that will work in your situation or not, but it is possible.
You can use the front or the rear port for the RH96.
You just need to build an adapter to go from an 1/8th inch stereo plug/jack back to DB-9.
I actually prefer to use the rear port for programming and for RH96 or software control use as I hate having the fragile cable hanging out the front of the radio. I think the only time you ever need the front port is for firmware and if you need to run a GPS AND a software app or the RH96.
Building a switchbox is also very easy as the RH only needs three signals so you can do it with a DPDT switch if you do not need to switch the ground. I myself have always used a plastic box so the jacks are isolated and then I use a 3 pole rotary switch to switch TX, RX and signal ground amongst the ports.
I have done what the OP is asking and it worked fine but I think I had to power cycle the RH96 when I switched from one 996 to the other.
Mine are the "T" and "XT" models though so it may work without a power cycle if both models are the same.
I built my switchbox to accomadate the two 996's and a 396XT but I never tried the 396. I see no reason it would not work though.