Is there a way to take a cutting of my rhodie to start a new shrub in a different place in the yard?
Azaleas and rhododendrons can sometimes be difficult to propagate with semi-hardwood cuttings, so be sure you take several if you go this route. These plants root best in winter, but you can still take cuttings from spring through summer from this year's growth. Remove all but the top 3-5 leaves, dip in rooting hormone, and stick in a 50/50 mix of sand and peat. Place the cuttings where they will get lots of light, but no direct sun, and keep moist. In fact, it may help to put a plastic bag (with slit for breathing) over top. By next spring, you can move the rooted cuttings up to individual pots and then transplant outdoors. They are also easily propagated through layering. Gently bend a branch to the ground (scratching away the bark at point of contact with soil), pin it place, cover with a little soil, and set a rock on it. Check for roots at the end of summer, and then sever it from the mother plant, putting it in ground during fall.
For additional information, this article will help: https://www.gardeningknowhow.com/ornamental/trees/tgen/how-to-root-cuttings-from-various-shrubs-bushes-and-trees.htm