I suspect it was a case of bluff and who blinks first. They have been talking for a while about Andy moving out of the lodge. Without doing royal duties he could not live in the royal lodge, he is not working for the priviledge. They brought in one of his daughters to try and negotiate. Andy refused to go quietly stating he had a watertight legal right to be there (probably why they offered to look after the 2 corgis).
So with I guess Camilla (who runs charities supporting women who have been sexually abused) and William who seems unimpressed with his uncles mid life crisis behaviour have drawn a line in the sand and he is no longer a prince.