There is no recognized breed called a "Dwarf Mini Rex," and there probably won't ever be. A couple of years ago, someone posted some pictures here of a couple of rabbits that they were told were Mini Rex, but that looked pretty much like Netherland Dwarfs with a Rex coat. Apparently, someone is having fun making up their own breed. I don't have a problem with that - that's how new breeds come about, after all. The problem is, the ARBA standards committee has stated that they will not accept any "new" breeds that can be described as an existing breed, just with a different coat or color, so these will just be a novel project for someone. They might even gain a following, but they wouldn't ever be showable.
According to the breed standard, the Mini Rex is a small breed, with adults weighing between 3 and 4 1/2 pounds. Those are the "true dwarfs," animals that have one copy of the dwarfing gene, and one copy of the normal growth gene. Any time you breed two such animals together, some of the offspring will get the normal growth gene from both parents; these are sometimes called "false dwarfs" and typically wind up weighing 5 lbs+ as adults. False dwarfs aren't showable, but some term the females "brood does" and use them in their breeding program; they can produce appropriately sized offspring if bred to a buck that has the dwarfing gene.
'