If I download Ding to my computer then would I have to do the transaction online right then, or can I call the person wanting tickets and she can call Southwest to book?
Your relative will not be able to book a Ding! *or* a SWA internet sale fare by phone, the best fares are only available online. They can be booked from a computer that doesn't have Ding loaded, but only by linking from an email containing a link from the Ding pricelist screen. (BTW, if you are an RR member, your CC info would come up when a fare from that screen is purchased, so I only advise doing this when you REALLY trust the person, and if you are sure that the computer they use is very secure. I'll send them to my spouse at work, but that's the only time I do it.)
Forget trying to call her and ask if the fare is OK; by the time you do that it will be gone.
Here are my ironclad rules for buying tickets for others:
1) Have the person write down the names of all passengers as they appear on their ID's. If the names don't match exactly, they may not get past security with them.
2) Have the person write down their CC #, with expiration date and the card security code, and also their name as it appears on the card. You will give this back to them along with the purchase receipt, and of course, you will keep it in a safe place in the meantime, and make no copies of it. If they don't trust you with this info, you cannot do the transaction for them.
3) Have the person write down which airlines they will not fly, which times of day WON'T be do-able, and how many connections they are willing to accept.
4) Have the person write down the maximum price, including taxes, that they are willing to pay per seat. Do a sample itinerary in advance (go through just enough purchase steps on a phantom ticket) to determine what the percentage is on taxes, and also what the passenger facility fees are per ticket, so that is not a surprise when the purchase is made. This should be a drop-dead price. If they need for the tickets to be refundable, that should be in writing, too, and make it clear that MOST tickets are not refundable or changeable, and that even when changes are allowed, they normally carry a fee.
You are asking that it all be written down so that you can be sure to get it right, but the real reason is that if she doesn't like what you do, then you have recourse to the written paperwork.
Whatever the temptation, DO NOT PAY WITH YOUR OWN CC! If the person can only pay cash, get it up front before you buy the tickets. Otherwise you are setting yourself up for the possibility of a nasty family rift.
If she doesn't trust you with the CC info to buy for them, advise her that she can book online herself using a computer at the public library.