I think it was better to move them and do provide them with a heat source. If inside they probably won't need it or may not even use it, but outside, likely your temps will be dipping in the 30s at night.
With a heating pad cave, I've found that chicks even though mostly feathered in sleep in the entrance, maybe to get a bit of warmth or possible using it as a feeling of security or place to hunker down. Make the cave high enough they can walk under, if they really need heat they will press their backs against it. If they just lounge, they will still feel a bit of warmth radiating down on them.
Hard to know if you should let the adults with the chicks or not. I've had non-broody hens that seemed a bit interested/curious for a day or so, but then chicks seem to get on their nerves. If Dixie was not mixing them with the flock yet, then she knew it was not time.
I do have a question. Dixie did not hatch and raise them with the flock - you just put her out with the flock and then you found her dead? Maybe I'm not understanding.