Think your relative really needs to take advice from her doctors on this, both about when it will be reasonably safe for her to fly and what she can do to reduce the risks further. (exercise in-flight, flight stockings, asprin and possibly statins come to mind - she may well have a high colesterol as well) If they advise that she needs to be active every hour (or whatever) and it's a lengthy flight she probably needs to ask for a seat where she can get up & down easily.
She certainly needs to be past the stage of any complictions from her operation. Hope it all goes well for her.