Sounds doable to me!
I recommend the Reykjadalur hike. It is fantastic, more or less mid way between Reykjavik and Vik. A fairly short hike to the river that is literally the temperature of a comfy hot tub. Shallow enough to just sit in and relax. Along the way you'll see many thermal vents, some hot pots, and waterfalls.
The Westman Islands was fantastic, with some good hiking available, right over the top of eldfell volcano! The ground is still warm, they say. I thought the volcano museum there was mind blowing, but if your teens wouldn't like it just make sure you read Rick's book or some other resources about the 1974(?) eruption so you can appreciate how unique this island and town are.
For bottomless teenage bellies, look for buffets at restaurants. The Soup Company in Vik isn't all you can eat, but you do get 2 helpings and the bowls are BIG.