Will installing an extender and leaving the primary faucet turned on cause pressure to build during the summer heat, causing damage the home's plumbing? Also, if this is not harmful, is a flexible hose or rigid pvc recommended?

It depends on the pressure. Try it and watch to make sure the extender does not leak or burst.

My water pressure - which I probably ought to check - is so high that we burst garden hoses ALL the time.

Let them set in the sun for about 2 hours without the water running, and BOOM!

To fix this, I'm considering a Pressure Reducing Valve to limit the pressure in the house. One more thing on my honey-do list.

Regardless, if you're extending your lines and using hose... be careful, if it bursts when you aren't home, this could be an expensive proposition, not only the water loss, but if you have a basement, it could get in there...