Sorry to hear about the loss of your chicken baby.
The OP identified the two mushrooms as close as one could hope for without rigorous examination -- fungal taxonomy is in a stage of renaissance at the moment due to advances in molecular biology and the genus Amanita is a jumbled mess. I'm afraid
muscaria is as close as you can hope for with this guy.
Fungi are ubiquitous and perform many vital functions in nature. As far as poisonous mushroom go, it is helpful to keep in mind that there are far more deadly poisonous plants than poisonous mushrooms. Also, the toxic compounds found in some mushrooms is, on a molecular level, large enough to not pose a risk of poisoning through merely touching or handling them -- eating them is a different story for humans and chickens alike apparently.
Quote:
When you pick a mushroom you are only picking the reproductive portion of the organism -- the fruitbody. The organism lives beneath the soil as a complex cellular network (known as mycelium). Picking a mushroom is not at all like pulling a weed.
In the case of Amanita -- and many other genera, these cellular networks are partnered with tree species in a mutualistic association that greatly benefits the trees, wherein the mushroom's mycelium bonds with the root tips and channels nutrients and moisture to the tree that would otherwise be unavailable. Oaks and pines are two families that take advantage of and depend on this. So I would be hesitant to use fungicides to deal with the mushrooms because you could inadvertently harm the trees the mushrooms are living with. For further reading on this check out the
Mycorrhiza entry at Wikipedia.
Picking and discarding the poisonous mushrooms is probably the best approach to dealing with the issue, although I understand why you would be concerned, I would be a bit worried if A. bisporigera was growing in or around my chicken coop.
Even though A. bisporigera is one of the few deadly poisonous mushrooms, I still think they are beautiful, here is one I photographed a couple days ago -- but I'm a mycology nerd and beauty is in the eye of the beholder I guess