Here is what I do for my 91 year old mother. Use a skycap outside the terminal to make arrangement for your elderly traveler. I suggest that even if you are not traveling that you accompany your traveler to the gate. The skycap can get you a gate pass to take your traverler through security even if you are not traveling. This is a service of southwest. Have the skycap take your traveler inside and wait for you to park car and return. The skycap should be able to get you a gate pass and everything, they make it very easy (and please tip them well for the service). You then can take your traverler to the gate in the wheelchair yourself without any problems. I do this all the time at my local airport so believe it should work for you.
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