Mold spores are pretty much everywhere and when given the right conditions will grow. The covered greenhouse created the perfect growing conditions and the moist peat pots are a good medium for it to grow on. That mold is not a plant disease concern. It is not particularly dangerous to your family either just from having it in the room. I suggest you remove the cover and allow the outsides of the pots to dry out a bit rather than staying constantly moist. That and some good air circulation should shut down the mold development. You can plant the transplants outdoors when they are ready.
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