You're right - you go in from the right front wheel well.
As for that thin wrench for removing the power cable, I've done this in the past:
1) When removing the alternator, disconnect the alternator power cable from the starter.
2) Remove the alternator with the approx 1 foot long power cable still attached.
3) Find two nuts that will go onto the alternator output stud.
4) Screw one down, then the other, and tighten them against each other.
5) Then, use two wrenches, one on the nut you're trying to loosen, and the other on the double-nutted thing on the top. Loosen the nut holding the cable down.
Reverse the process to put the wire on the new alternator.
(Of course, you can do what I've subsequently done - buy the wrench and have a machine shop shave it down to about 0.060" Works like a charm!)
Good Luck!
PS - Replace the battery also. Weak batteries kill alternators, and weak alternators kill batteries. Cheap insurance!