if the solder iron you picked up is an always on unit and not a gun you should be ok with 25W, if it is a gun you may need a hotter iron. I used a 50W gun and had the module back in my car within thirty minutes. Check your solder, ideally you want a rosin flux-core, as an acid core can damage the circuit board if you apply too much. As previous posters have said make sure you are not melting the solder on the iron, but on the leads themselves while still applying heat to the leads. I cleaned up the old solder with an emery board prior to soldering (one of the leads had too much built up already on what was blatantly a cold solder from the cracking). The leads run to the huge pins that power the module so it will take quite a bit to heat them up. You are correct that you DO NOT want to connect all three leads as that will short out the board and you will have to purchase a new one.

As a side note if anyone near Wilmington NC needs or desires their RCM re-soldered or just inspected feel free to PM me.