If you're facing the task of transplanting a rhododendron, it can be a challenge, but most rhododendrons, even large ones that have been in place for many years, can be transplanted successfully. The exception is rhododendrons that are planted so closely to other plants that the roots may be intertwined. In most climates, the best time to transplant rhododendrons is in early spring while the plant is still dormant. In warm climates, transplant them in late fall so they have plenty of time to establish before summer.
Shovel a circle around the rhododendron, leaving several inches between the bush and the circle so the roots won't be damaged. It's a good time to enlist help, especially with a large bush. Give each helper a shovel, and coordinate your movements, with all shovels levering the shrub out of the ground at the same time.
Slide the bush onto a tarp, again enlisting help for the task. Use the tarp to drag the rhododendron to its new location, and plant it as soon as possible so the roots don't dry out.
Dig a new hole about half again as large as the rhododendron's root system. Mix in a few scoops of compost and peat moss. Add a dose of transplant fertilizer, following the manufacturer's directions.
Loosen the rhododendron's roots slightly, and plant it in the hole with the trunk at the same soil level that it was previously. Turn the plant so the most attractive side is visible.
Let a garden hose run slowly into the hole. Replace the soil as the hole fills with water, tamping it down around the root system. Add 2 to 3 inches of mulch around the bush to keep moisture in.