Beerman,

Next to sailing, Iceland is one of the most beautiful places to travel. I spent a week there a couple of years ago. Fantastic. Glaciers, natural hot springs, Geysers awesome hiking.
We went around the south side as far as Hofn. Then over the top on F35 and to the north side and then back to Reykjavik. With 10 days you might be able to go all the way around, but you may be rushing it. A lot of the neat stuff is off the beaten path - 4 wheel drive style. It's slower than driving the ring road but worth it.

If your family likes horseback riding, that's a must. Their horses have a 5th gait very unique.

You will love it.