We ended up with a hole in the wall, about the size of the palm of the hand. The wall is hollow. How could we fix it?
I would get two bits of wood or stiff card twice the length of the hole but less than the width of the hole.
Put a screw in each piece of wood, close to the middle.
Make sure the reverse side of the hole is flat and apply a strong glue to the back of the hole and the face of the bits of wood.
slide the bits of wood into the hole - one at a time - and position.
Then with a bar and two blocks use some string to keep the wood in position by tying the screws to the bar.
Once dry, fill, sand and re-finish as necessary.
Edit based on Jimmy's comment: A variation that will be quicker, if you don't have time for the glue to dry (or to avoid glue at all), is to run screws through the wall and into the wood/card backer, adjacent to the hole, to secure the wood/card backer in place, driving the screws flush with the wall surface. Patch the hole and over the screws at the same time.