Driving a 25 foot rental RV to Florida with large dogs (2 drivers)

Can someone with much more experience please propose a route from Plainfield IL to Cape Coral FL that bypasses the mountains in TN (Lookout Mtn) and avoids ATL traffic?  We are leaving at 3AM on 5/21 and need to be in Cape Coral by 1PM on 5/23.  We will need to take a few short breaks and plan to change drivers as needed. We will spend the night on the RV both nights.  

Thank you in advance for your help.