Hi Ford,
Sounds like a good problem to have! 🙂 And I’m glad you have found tentative housing on the South Coast– are there really still places available for 4 people on the south coast for 220 Eur a night?
Is your concern that 13 days will be too much for the kids, and that they will be bored? As long as the kids are up for exploring (like my 7-year-old is) I think they will have a good time. But my kids are happy to take an hour to explore a black sand beach, or a cave, or whatever we happened upon.
You may also be asking if it’s worth the extra time and expense to do the whole ring road? That’s a tough call. We did enjoy staying in a new to explore town every couple of nights, and there will be fewer tourists as you get past the south coast. You also will save on having to backtrack to your apartment in Reykjavik most nights.
But 8 days to explore will still be great. You can take a (long) day trip up to Snæfellsnes if you wanted. Perhaps you could spend a couple of days on the south coast and a night up in Snæfellsnes? That gives you the opportunity to explore new places without committing to the longer trip.
If you do the longer trip, make sure you understand the conditions getting to Askja. I think there are some river crossings.
I’m not sure if I helped at all. Let me know what you decide!