When you say Rose of Sharon, do you mean Hypericum calcynum (multi-stemmed, yellow flowers) or Hibuscus syriacus (various coloured flowers, often pink or blue or white or mauve, but certainly not yellow, usually single stemmed)? Because both are commonly called RoS and are quite different plants.

If you mean the Hypericum, then it is close to impossible to kill, and the plant tends to regrow very easily from root fragments. Dig a bit up and shove it it in somewhere, anytime, anywhere, and you will have as many new plants as you like. You'll have difficulty stopping it growing where it originally was unless you apply strong weedkillers.

If you mean the Hibiscus, then smaller plants can be moved fairly easily, best time is in spring, and prune them first. Larger plants have a large rootball that will require mechanical assistence to dig up/move, and are slow to recover. An alternative approach to moving a large plant might be to take cuttings (research how/when best to do this), propagate new plants from the cuttings for the new locations, and dispose of the old plants when the new ones are established.