Easiest way to deal with a,"Problem Neighbour", is to let them know,(Subtly), that the more they try to feck you about, the longer the job is going to take.
After your plans have been passed, "It is going to happen". Once they get over their initial objections being cast aside, they will try to make things awkward for you just for the sake of it. Dont, "Rise to the bait", but just make it clear to them that the job will take longer and the horrible, nasty builders will be disrupting their idyllic lives for a bit longer too.
"Simples".