Normally I'd say "Yes, of course look for a higher paying job!!" but based on everything you said...but after reading your whole story I would say you should stay put. It sounds like you have the perfect situation for someone who has three young children. I'd honestly consider staying there as long as possible given their level of flexibility to allow you to work and attend to the needs of your children.

This keeps you from paying for childcare or using sick days to take kids to appointments. Your boss sounds literally amazing, like a boss most people would dream of having.