I think you mean an
ECV (electronic convenience vehicle) rather than a power wc. To answer your question, yes, you may be able to get an ECV at the WS entrance. Whether you in fact can do so is another question, esp at peak season. If you wish to try this, I suggest getting there early (park opening time at the latest at a non early entry park) and bearing in mind that someone in your party may have to run across to see if you can get one at the main entrance (the wc station is smaller at this entrance) or push a wc in the event that they are out.
I am not sure what your dad's feelings are re renting offsite and why he is against it, but I highly suggest renting offsite. You do not have the angst of availability, esp if you are traveling peak season. You can park hop and know that you are set at the second park. You can go to Downtown Disney or other non-park places and use the ECV. You can drive with the ECV right over to both MGM (there is a path that goes past the Boardwalk to MGM) & Epcot. Also -- and this is key -- the offsite rental
ECVs are so,so much better. You can get a 3 wheel style that is a TON easier to drive than the 4 wheel WDW rentals. Backing up into a spot at an attaction is a piece of cake with the offsite rentals. And you have it at night, and if you are at the Beach, you may well want to go to the Yacht or Boardwalk for dinner.
I cannot tell you how many WDW rental users stop me and ask about my ECV when I zip effortlessly into place at an attraction or whatever and they are going back and forth trying to park. The cost is either the same (for a daily rental) or less (if you rent for more than a few days -- for example, it is $199/week from Walker). WDW wants ECV users to be slow and cumbersome so people do not abuse them or cruise thru the parks. The user, however, pays the price as the 3 wheel ECVs are totally superior.
All that being said, if your dad is comfortable with the idea of the WDW ECV, more power to him. Take it slow generally and have him take his time. Avoid the MK your first day as that is the most crowded with the tightest spaces and thus not the best place to get confident using the ECV. Remember to park thinking of how you will get out (back in so you can drive right out). If he can transfer to a regular seat. drive the ECV to face the exit at attractions and then sit in a regular seat if he has trouble in tight places. And I cannot repeat this enough -- get there EARLY. The ECVs go fast.

Cupcake