Don't know much about fire ants. I last saw them during a visit to Texas in the late 1980's where they climbed up a stick I leaned against a tree within seconds. They haven't made it up north yet. I like the goat idea but I don't know how well the could would get along with the fire ants. Since fire ants are invasive you could kill them or have an exterminator kill them with a clean conscience. The poison ivy could be sprayed or hand pulled if you suit up properly. Clip it where it is climbing vertically on trees to reduce seed production and to save on spray. You just need to clear enough area around your pile to be able to work safely. I don't recall carpenter ants being big biters but you might not want to introduce them near your house. Maybe a different location for the pile would help if that is possible. An enclosed bin migh help with these issues if you aren't already using one. Even if you never use the compost you are helping to keep waste out of the landfill.

Hello...we don't have fire ants here in Maine so I can't comment on them. We do have carpenter ants...never have seen them bother my compost at all.
I would spray the oak and ivy with roundup a time or two if your subject to gettin' the rash and itchy's.
Gardening will put you in close contact with these things and probably other things as well...like snakes and maybe scorpions in your area...so don't panic. Think of all the nice veggies and fruit you can enjoy that you wouldn't have otherwise...if you decide to quit. Franklin

Carpenter ants, and most other ants, are not a problem and need have nothing done to control them outside of your house. Fire Ants, however, do need to be controlled and Texas A & M has the best information about controlling them.
Poison Oak and Poison Ivy, as well as Poison Sumac, all need to be eradicated from where you work and play, but do so with care and do not make contact with it. Wear good protective clothing and gloves and be sure these are kept away from any other family members clothing (some people throw this clothing away afterwards). This is one material from your yard that should not be composted or recycled on your premises, bag it and trash it.
It may take a while but you can tame that area.

Here is a link that might be useful: Fire Ant Control

Thanks guys for the information. oldtimer I'm not quitting with the composting, it just won't be a pretty compost pile like some of the photos I see in this site.
If I decide to house a small goat, I have a larger dog kennel that I intend to keep it when it is not outside "working" eradicating the poison oak, poison ivy and, yes, we have poison sumac too, the goat will have to stay in the dog kennel. I will be outside to make sure the goat is safe for we have seen coyatoes walk through the yard. The goat will be borrowed just for the purpose of a safe way to get rid of the poison mess.
Kimmsr, I went to fire ant control site and realized that we need to fight the ants in the fall, probably all year in North Ga area. The fire ants were here when we brought the property, which surprised me for it was a vacant hill top property, but the previous owners had a tomato garden up here. I suppose the ants could have been brought in to the area in tomato plants?
Anyway, thanks guys, and I will be careful when fighting the poisons out there. I have to suit up to work in the yard, complete with long sleeves, long pants with my socks over the top of the pant legs. Plus, of course gloves. Reason: Ants love me, they seem to track me down, plus I'm sensitive to poison sumac and hubby is very sensitive to the other two. The socks pulled over the top of the pant legs is to ensure no ants crawl into my clothing. We have mean fire ants in GA.