This is possibility a serious condition, which you should show to the doctor immediately as she seems to have suffered from some sort of an insect bite or an allergic reaction to some kind of plant like poison ivy. You need to note that some kinds of spider bites can cause tissue necrosis, which can end up being fatal and cause other sorts of complications as well.
A rash is typically an allergic reaction that is basically an inflammation. Inflammation is the immune system’s response to a foreign body and begins with swelling as you can see in a rash and the secretion of mucus as well. However, where things get a little confusing is the legs turning blue. Blue usually indicates that the tissues are not getting enough oxygen and this is a rare occurrence after a rash unless it is either an extreme allergic reaction or the effects of a spider bite. You should also explore the possibility of your daughter having touched poison ivy in the neighborhood. From the symptoms that you have described, there is a possibility that she might have been bitten by a Recluse spider. This spider bite is sometimes painless and the symptoms end up taking time to manifest themselves. In children, the bite of a Recluse spider can cause the rash that you described and also a condition called loxosclelism. This condition is typified by the leakage of hemoglobin into the surrounding tissue – this sounds quite a bit like the blueness that is occurring on her leg.
The assumption would be that you would have already taken her to a hospital as this condition rapidly deteriorates; however, if you have not then you must do so immediately. Poisonous spiders secrete two kinds of venom neurotoxic venom and necrotic venom. Neurotoxic venom is a kind of paralytic agent that works by blocking the sodium channels of the nerves thereby preventing communication between neurons. It is this paralytic effect that spiders use to immobilize their prey. Necrotic venom causes massive cell death of the dermis or skin. In contrast to normal cell death, where the immune system overwhelms the dead tissue and replaces it with new cells, in necrosis, the immune system does not respond and the skin cells in the area end up dying while still on the body. This can further lead to other situations like the pathogenic bacteria taking over and poisoning the blood as well as renal failure.