The problem IS that you're inserting the 2nd key into the ignition. Just as the "other" instructions state...
you start the 2nd key on STEP 3.
(BTW: thanks for actually writing out in detailed steps what you were doing instead of writing that you "followed the instructions". 
Your details reveals to us (not there with you) as to what you were doing incorrectly.) 
When you insert the 2nd key into the ignition...you will erase the programming of the 1st key. This is intentional in that a stolen remote key can easily be slightly sidelined by preventing it from having the capability of "remotely" unlocking your vehicle. It can still manually unlock (of course)...but if you reinitialize your remaining remote key, then use the OBC CODE feature...you can prevent someone with your stolen/lost remote key from remotely unlocking & being able to start your car until you can get the vehicle in to the dealership to have the stolen/missing key "barred"...at which point you won't have to use the CODE feature to prevent them from starting the car.
Note that
STEP 6 says to go back to
STEP 3 to program a 2nd remote key...and it's inferred that you start with the "press & hold" instructions since you are NOT told to INSERT the key into the ignition:
And as far as recharging your second key...it can take up to at least 30 hours to fully recharge a discharged key...but you can get it to operate approx 15 times if charged for at least 30 minutes.
KL R is the equivalent to
ignition position 1 . . . if you want to give the 2nd key a full charge and you have a battery tender or charger (preferably with a 2-5 amp selection)...hook it up to the jump start posts in the engine bay (positive post under the cover & negative to the hex bolt on the left (driver's side) fender) over night so that you don't drain the battery while the ignition is on.