Here's some info from the University of Mich.
European rabbit rabbit
Kingdom Animalia Phylum Chordata Subphylum Vertebrata Class Mammalia Order Lagomorpha Family Leporidae Species Oryctolagus cuniculus
cottontail rabbit
Kingdom Animalia Phylum Chordata Subphylum Vertebrata Class Mammalia Order Lagomorpha Family Leporidae Species Sylvilagus floridanus
The two animals are different species, just like horses and donkeys, or lions and tigers. I've heard of several people in Alabama who have bred cottontails with domestic rabbits.
The behavior of your Rex sounds like a rabbit I had many, many years ago. Most loving rabbit you could imagine, until she had young. She would growl and stomp her feet if you went near her babies, and if you ignored her, she'd bite.
I'm betting in 3 or 4 weeks you'll have baby rabbits running around. I'd suggest putting a fence around the burrow so you can catch the little critters.
Kenneth