I would suggest that you try the agencies in Little Rock. I don't live in Arkansas, but I do this kind of work. Here the agencies are located in the big cities but have cases all over the state. I live in a rural area an hour from the nearest city and get cases near home. Some agencies don't necessarily advertise or specialize in pediatrics but will take on the case, especially if they have nurses in the area.
That said, pediatric homecare is an area with a huge shortage. Parents never get the amount of help they really need. But, whatever you can get is at least a break. A good agency will run ads in newspapers and online to recruit a nurse for you. Ask about this before signing a contract with a new agency. In advertising they should stress the positives. Many nurses don't do this work because they assume the kids are terminally ill. This is not usually the case, so it pays to get the word out for your child.
I wish you all the best. I know from experience how difficult your situation is.