Your sister should take him. If she parks in the short term parking garage, she can walk with him to Level 2, door 4 and explain to the skycap what he needs. Or, assuming that his ticket is already printed out, she should pull up to door 4, leave dad in the car for a minute and go in to the wheelchair assistance area and get him the chair and help he needs. I believe that you can talk to a skycap. You should not just send him by car service because the system changes and who knows how it will be when he goes. Asking him to wait in line to get to a customer service agent is silly.

Make sure that the airline knows that he will need transport upon arrival. The return trip should be a little easier. Again, make sure he is on the list for wheelchair transport and the pusher will take him where he needs to go.
I use my own chair when traveling but I've watched this process happen with others. Good luck.