I'm in Western Arkansas, and these are red, hollow mushrooms with a brown slimy coating that popped up in our mulch, roughly a half an inch in diameter and they have grown several inches tall. Is there anything specific that I can/should do to these things? I have young kids and pets that I assume I don't want eating these things.
This looks like a type of stinkhorn fungus. They commonly pop up in urban settings, including mulched areas, and can come in many different appearances. The slime on these mushrooms is used to attract insects and flies which will disperse their spores. They are found in North America including in temperate and north-temperate climates. According to MushroomExpert.Com these mushrooms will not hurt you, your children or pets.
Specifically, the stinkhorns in your photo look like Mutinus elegans to me.