Apple tree pruning/relocating

The general advice is to move plants when they're dormant (winter). I moved a favourite apple tree in late summer when the sap was in full flow, and it died

Pruning in summer should only be reserved for trees which are putting on too much new growth.
Pruning weak trees in summer could kill them, or at the very least it will knock the stuffing out of them which could take years to recover.

Trees have just invested lots of resources into producing leaves and shoots. The early-summer leaves are built with the winter reserve which has bene stored in the roots.
They have now expended all their reserves and need to use those leaves to collect sunlight energy while the sun is strong and the temperatures are warm.
If you take the leaves away, they won't have had time to gather much sunlight energy, and won't have much of a reserve with which to replace those lost leaves.

As Two Sheds has said: moving apple trees in summer is a delicate operation and the key to success is to lift the tree carefully from all sides using a fork about a foot away from the trunk, and, once you start, it must be quickly replanted before the roots die from sunlight exposure, heat and desiccation.

In other words: everything must be planned in advance and the new planting hole dug before the tree lifting starts - and the tree must be replanted in its new location within a few minutes. Just 15 minutes out of the ground in this weather will cause serious root damage.

Very vigorous rootstocks may cope better, as may dwarfs because you can lift the whole of a dwarf's tiny root system without breaking many roots.

For the tree's health, I would also suggest having used TAP WATER to thoroughly water the new planting site about 24hours before the transplant takes place.
Tap water is clean and chlorinated, which reduces the risk of damaged roots becoming infected by root-rotting fungi often present in water-butt water.
Also, by watering the site beforehand, the soil will be nicely damp. Easy to work on, but also nice and damp for the trees roots. This means that watering after transplant will not be necessary.
I have found it best not to water immediately after transplanting (give it a couple of days if possible) as watering tends to make the ground too wet/heavy, encouraging fungal spores to germinate, which then attack the damaged roots and possibly begin a chronic incurable root infection which slowly kills the tree over a period of several years as it gradually tracks - unseen below ground - up the roots to the trunk.