Can you tie the trip to a special event? Her birthday for example, or a child's birthday, or a holiday? So: "best gift we wanted to give you is an opportunity to spend some time with the kids."
Sending a ticket or money may mean pressure that she has to come and if she does not buy/use it or cashes it in you are out the money. Maybe there is a way to "hold" a ticket for her. If she decides to come she has to call the airline to arrange it but it is charged to you and held by the airline until the flight. That will give her flexibility on when she wants to visit and you will get a refund if she does not follow through.
