Your animals will travel in the hold and be transferred to Icelandairs' animal processing facility at Keflavik which is fully equipped to deal with caring for them on layovers of any length (it's the same facility that takes care of animals shipped as cargo).
I experienced this involuntarily, when a delay and subsequently missed connection turned a two-hour layover into an overnight stop. I had a dog as checked baggage who got fed and exercised - there were zero issues.

The layover restrictions for service animals are in place because these travel in the cabin and are prohibited from leaving the transit area under Iceland's extremely strict biosecurity rules (this could simply be remedied with a airsde pet relief area at KEF, but I guess there's not enough demand).