If the at-fault driver has full coverage who pays for a rental car?

In Texas, The At Fault Driver's Liability portion of their policy will pay for rental car usage at a maximum of 20 dollars per day for up to 30 days or until the such time as the Insurance company has made a reasonable offer to settle, whichever comes first. This rule will vary by state.

If the at-fault driver goes under their own policy to get repairs, they would have to have bought rental coverage to get a rental set up.