I agree that, if the fire WAS an attempt to cover up some evidence of wrong-doing, a space heater seems like a really risky way of doing that. The whole issue with unattended space heaters is that they're dangerous b/c they *might* cause a fire -- which means, on the flip side, that they might NOT. If there is something that you really want gone, I'd think you'd use a more sure-fire method. That makes me put more stock in the idea that maybe there really IS a series of coincidences at work here? Like, these three separate events: the date/Chad, the fire, the disappearance -- are all unrelated; Chad was just a date, the fire was an accident, the disappearance was intentional but not related to the other two. That leaves the question of what would drive a young mother, with apparently strong family bonds & a decent relationship with the father of one of her kids, to voluntarily split with her kids with no warning like that (and maybe with a bag of clothes, etc, in the back of her car).
I hope they're found safe.