If she is worried about the airports, procedures, the passports and baggage and so on, the absolutely best option for this lady would be the Assisted Travel scheme. If the OP helped, they'd both have to struggle through, with the OP helping the lady with her baggage, walking long distances at the airport with her, helping her through customs and immigration and so on. If the OP DOESN'T help and the family uses the ATS, here's what happens:
The old lady will be met at check-in, whisked into a wheelchair if mobility is an issue,her hand luggage sorted, fast-tracked through immigration, taken to a lounge with other people who are being helped, then whisked to the gate by golf cart at the right time to get her plane. The attendants will give her special attention on the flight. At the stopover, her connecting plane will be alerted and she will again be whisked there by golf cart. They will make sure she doesn't miss her flight. At the other end, back into the golf cart or wheel chair, then fasttracked through customs and immigration, her luggage collected, then lady and luggage will be delivered straight into the arms of her family. She won't have to carry anything, she won't have to walk, she'll be with an experienced helper all the way. And it's free. My father did this from Australia to the UK and back a few months ago.
The OP couldn't possibly provide this level of help even if she wanted to, so there is no need for the OP to have her flight made harder or to be guilt-tripped.
I love suocera's work on this thread.