Ford Taurus Rear Brake problem

Well I can't give you specific advice but some general advice.
The reason you have to turn piston back in is because the hand brake
mechanism is built into the rear caliper. Generally with Japanese
cars you can use the square tool to turn the piston back in. I worked
on a VW jetta that also turned in, but the square tool wouldn't fit
properly so I used another tool like a screw with two bumps at end.
You usually turn it in clockwise. On american cars I have worked on
sometimes I had to disconnect the handle at back of caliper to push it
in with a clamp (GM). I don't remember doing a Taurus.
Sounds like you may have turned the piston off the screw
mechanism inside it. You might try to remove the caliper completely
from the car and try to apply pressure to the piston while turning it
clockwise or try counterclockwise. Otherwise you might have to try to
disassemble it to see how it works. Maybe you should buy a good
manual on the car.

I usually use a largish carpenters "C" clamp to push a pison back in.
I don't understand when you say "turning it (the tool?)both ways". You
only want the tool to work the piston in, generally tuning the screw
on the tool clock-wise.
What is coming off? Nothing should come off except the old pads and
reatainers and anti-rattle springs

(I'm getting small amounts of

Getting brake fluid from your caliper is not good, it should not leak

Sure sounds like a bad day. The only reason for pushing the pistons
back is so that when you slide the caliper over the new pads, the
caliper will fit.
Sometimes the pistons will sieze , and there is little you can do
about it except to change the calipers and then bleed the brakes.Were
the rear brakes operational? Why are you changing the rotors? Were the
rotors warped, scored,
damaged? This could be a sign of siezed calipers, especially if you
are using massive force to drive them back in.

sounds like you have unscrewed the piston from the caliper. You might get lucky and screw it back but will probably damage the seals.

...

If your leaking brake fluid you probably scrooged the works by now.

Next time, before you remove the old pads and rotor, jam a large
screwdriver in between the old rotor and pad, open the bleed screw,
put a clear tube on the end and put the end into a jar, and
use the screwdriver as a lever to force the caliper piston back. Make sure
to tighten the bleed screw as soon as the piston is all the way back in.

Ted