Is is possible to move a drain and water supply in a concrete floor with radiant hot water heating throughout?

Not safe to try unless you have a good set of plans showing where the tubing was laid.

Ballengerg said it. You will most likely rupture some heat lines if you don't know exactly where they are. Even if you do know where they are, you are likely to have a serious project on your hands. If you must do this, I would wait until summer(when you don't need the heat). Shut down boiler, and drain system. Very carefully break up concrete, there will most likely be damage to heating pipes in concrete. Just make sure you know what type of pipe(tubing) it is, and have repair couplings and extra tubing on hand. Before pouring concrete, refill and bleed boiler system and check for any leaks in the area of repair. I would wait at least a week with boiler system pressurizes before pouring new concrete. The last thing you want is to have to break up more concrete to fix a problem with the floor heat tubing. Good luck and please let us know how your project turns out if you decide to do it this way.