We had a week in Iceland the second week of April 2014. For some of that time, we rented an all-wheel-drive Chevy SUV from Hertz in Reykjavik. I don’t remember, but maybe it was a Traverse or an Equinox - not an off-roading truck, but having the 4WD was reassuring (more on that later). You’ll want to determine Iceland seatbelt laws for children, too (again more on that to come).
This was all before Rick Steves had an Iceland guidebook, and we mostly used the Lonely Planet guidebook. We also booked a private tour for a couple of days, where the driver/guide led us on a glacier hike and went as far east as the Jökulsárlón lagoon, for the night. That year, there were really no big masses of ice floating in the lagoon, and there was just one piece of blue ice, maybe 5 feet long and 2 feet high, on the shore. That was disappointing!
I’m not familiar with many of the things you list (were they there in 2014?), but I will say that we chose the soaking and sauna opportunities at the Fontana baths, near Thingvellir, and not Blue Lagoon. We had one day for driving onto the Snæfellsnes Peninsula while still staying in Reykjavik, which was a nice day trip, but we hardly made a dent into what more time would’ve allowed.
I posted this previously on this Forum, but I’ll repeat a couple of driving experiences on that trip. Be prepared for fierce winds that can gust unexpectedly, which can affect the handling of both your vehicle and any approaching you on the relatively narrow 2-lane highways. We had one section of road with several prominent signs warning of potential dangerous crosswinds, but signs weren’t ubiquitous.
The other situation happened in late afternoon, just after we’d stopped to view the Kerið crater. The roads had been dry all day, and it was still a while before sunset. Visibility was good. Suddenly, a strange vision ahead seemed to be something white, spinning in the air. It turned out to be a VW sedan that had just hit black ice on the road, and become airborne, flipping and spinning. It was a 5-passenger car, but had 6 passengers. That means at least one wasn’t wearing a seatbelt (which, we were told, may have led to criminal charges for the driver, who was operating a car under that situation). At least two people were ejected, and the one the car landed on top of died, following transport to the only emergency hospital in the country, in Reykjavik. I immediately called 112 (Iceland’s emergency phone number), while my husband and others pulled the victim out from under the car and tried to resuscitate him. After the police arrived, they had us stay for an extended time, collecting information. The restaurant at the hotel was closed by the time we got back to Reykjavik, in the dark, and shaken. The black ice was unexpected, and not discernible until we were actually on it, later on.
I know that Colorado requires proper child restraints for kids of various ages/sizes. I don’t know about California, and maybe you’re already doing this, but I believe kids of certain ages or size also must be in the back seat. Ensure what Iceland requires, above and beyond what may be your regular practice with your 7-year-old. Be prepared for adverse road conditions in April. Enjoy Iceland, though, an awesome place!