Do the parents have pedigrees? If they don't, then you technically can't call them purebred (even if in reality, they are purebred).
Also, just some FYI on genetics, you can't have a standard rex and a mini rex in the same litter if the so called parents are purebred. Standard rex and mini rex are two entirely different breeds. For example, that's similar to saying you got a labrador retriever and a chihuahua from a litter that had purebred chihuahua parents. Not to mention a combination like that is impossible. (And even if this combination would be possible, the labrador wouldn't be called a labrador because it's parents weren't labrador, making it a mixed breed.) So even though an animal may "look" like a certain breed, if it doesn't have purebred parents of that same breed, not to mention those parents have to have at least a 3 genereation pedigree stating that they are ofall the same breed, than you can't call that offspring the name of any actual breed.
So, back to topic, lol. If you say the parents are purebred mini rex (and they have an actual pedigree to prove this) and the siblings are mini rex, than your rabbit is mini rex.
If the parents don't have a pedigree, there is no way to prove that they are purebred, making your rabbit and it's sibling, mixed breeds. They may look like mini rex and have mini rex in their background, but judging by your rabbit, they either have very bad breeding, or there is a standard rex thrown in their background somewhere.