Rental car questions?

my wife and I are about to go on a trip to southeastern oklahoma to visit my family. Now a great deal of my family lives on dirt roads (highway contracts). We plan on renting a car at the airport, and after reading a bit would taking a rental car onto these dirt roads incur extra charges or be a violation of the rental contract? also, what are good cars to take down these roads? See i drove my ford focus down these roads before and had a problem with under steering, i would like to avoid this problem again since i had to spend a lott of time correcting my driving and driving about 5 miles an hour to keep from under steering in every single corner.