I would dig the new hole first and then dig up the plant when you can move it. Water it the day before you plan to dig it up. It reduces the stress a little more, especially when one digs up the old plant and -for whatever reason- delays planting on the new location. Get as much of the rootball as you can and keep it moist. Cover the soil to keep it moist and intact. Do not let the leaves wind burn on the outside of a pick up truck, if you can help it.

You need to be mindful of the clauses in real estate sales contracts that govern the shrubbery and trees planted on a parcel of real estate. I think the ornamental horticulture is considered a part of the real estate that is being sold. Therefore, the seller of the real estate is obligated to leave the shrubbery and trees in place, exactly as they are, unless special legal arrangements are made.