I don't know what type of mushrooms they are either. But my children 'homesteaded' our backyard when they were kids. Mushrooms grow on decaying organic matter so eliminate the source. Watch out for other plants that may look edible to your kids, like Poison Hemlock which looks exactly like carrots.
I actually planted a grazing garden for my kids out in the family orchard. So they had access to all the fruit plus zucchini, asperagus, carrots, Miner's lettuce... I was careful to keep that part of the yard clear of anything harmful.
Daisy
