Welcome to this SCLS virtual community, even though you are joining in very unhappy circumstances.
As you will read under Disorder Details, "When too much fluid is administered [during the resuscitation phase of a capillary leak], the result is excessive swelling, and the patient may well require surgical decompression of the limbs. In this procedure, known as a fasciotomy, the skin of the arms and/or legs is incised to release the compressive pressure the retained fluid is having on blood flow to and from the extremities."
I have undergone this procedure 3 times, and after the first time, the orthopedic doctors also wanted to amputate my legs, which were seriously impacted. However, my wife got a second opinion from a senior vascular surgeon who advised against amputation, and so she refused to give her consent. There followed a number of operations (by a surgeon who was not involved initially) to remove the necrotic (dead) tissue that was posing the risk of serious internal infection, and the end result is that today I still have my legs and walk pretty normally, even though I did have partial loss of muscles and nerves.
The moral of this story is that your family should urgently get second and third opinions, from vascular and orthopedic surgeons, on the real need for an amputation, because there are many ways to fight infection (which, incidentally, could be the hospital's fault unless it is from necrotic tissue). An amputation cannot be reversed, so it should be an absolutely last resort.