My White/Rogers 1F94-371 t-stat died a few days ago, and I have guests at the house this weekend who need to use the t-stat in that part of the house. The wiring at the old t-stat was:

E terminal -> brown wire jumpered to W2 terminal
C terminal -> blue wire (from wall) and black jumper to C terminal on far side of t-stat
R terminal -> red wire (from wall) and red jumper to R terminal on far side of t-stat
W3 terminal -> not used
W2 terminal -> white wire (from wall) and brown wire jumpered to E terminal
E2 terminal -> not used
W1 terminal -> not used
Y2 terminal -> not used
Y1 terminal -> yellow wire (from wall)
B terminal -> not used
O terminal -> orange wire (from wall)
G terminal -> green wire (from wall)

The Hunter 44660 has the following available terminals:
G terminal -> (assume it gets green wire from wall)
Rc terminal -> no indication what this is for
Rc1 terminal -> no indication what this is for
Rh terminal -> no indication what this is for
Y/O terminal ->
W/B terminal ->
Y1 terminal -> (assume it gets yellow wire from wall)

The manual included in the package has literally no wiring diagram, although I did find one in the user manual online. It says the following:

RH / R / VR / 4 is 24v and goes to RH (assume R goes to RH)
RC / VC is 24v cool and goes to RC (don't have RC or VC)
Y/ C* / M / O is A/C compressor and goes to Y/O (but notes that any wire labeled "C" should not be connected to the t-stat) (have C and Y and O -?? )
W / H / B is heating and goes to W/B (?? )
G / F is fan and goes to G (assume G goes to G)
Y1 is heat pump compressor and goes to Y1 (assume Y1 goes to Y1)

After hooking it up based on my assumptions above, I have no A/C and a cranky mother-in-law. Any help will be greatly appreciated.

We normally telll people who buy Hunter stats is to take them back for good reasons. They don't last. They have good usefullness as a paper weight. You had the first indication by looking at their manual.

I don't know what Rc1 is either.

I can tell you that Rc gets connected to Rh which gets connected to your old R wire.

Y/O
Y turns on the compressor. O is used when the reversing valve needs to be powered in cool.

W/B: W is used to turn on heat; B is the complement of O. Used when the reversing valve needs to be powered in heat.

Y1, Y2 on your first stat follows the right convention for two stage cool. W1,W2 and W3 are the convention for 3 stage heat.

The Hunter would not use C because it is powered by the battery.

Once "C" is removed from the equation, any wire can be connected to any other wire without fear of major problems. The compressor should be allowed to rest because it can't start under high head pressure. It may pop the AC MAIN fuse.

Basically, between R and C, there is 24 V all of the time. C is the common of the transformer.

Rc and Rh have been added to stats to accommodate a separate transformer for heating and cooling, that's why they are jumpered together for a system that uses an R.

Advise: Take the stat back.