The broken gene has been linked to gastrointestinal issues and charlies are more likely to have those issues.
I know of one study (using Checkered Giants) that found that
all Charlies have those issues, the only difference being the severity of the symptoms (which tends to increase with age, even in individuals that seem only slightly affected when young).
Generally speaking, color should be the last thing one considers when choosing a breeding animal. First and foremost, you want good type and a good coat, with color being part of the equation only to avoid "whoops" colors (my term for those colors that aren't showable, or are poor versions of a color due to the lack of certain key genes (Chestnut/Castor and Orange/Red being examples of the latter).
When breeding Brokens, one thing to bear in mind (separate from the Charlie issue) is the amount of white on the animal. You want an animal to have a nose marking, color on the ears and around the eyes, and between 10% and 50% color on the body - more or less than that is a DQ. Some people are breeding lines that are solid colors only for many, many generations. When you breed a Broken to a solid from that sort of breeding program, you may get "booted" Brokens - animals with just a little bit of white on the feet and chest, and maybe on the face (the bunny in my avatar is a booted Broken Red). The Broken gene sets the pattern, but exactly how that is expressed depends on some "helper" genes, and a rabbit that doesn't have Brokens in its ancestry may not have the right helpers. This seems to happen a lot in Mini Rex, so if you are breeding Brokens, you want to breed to solids that have Broken relatives.
A chocolate Otter doe (her parents are outstanding, she is a very poor representation of the breed, but breeder said she'd be a good brood doe).
By "very poor representation of the breed," do you mean that she's a false dwarf? False dwarfs happen in all of the dwarf breeds (as you doubtlessly know from breeding Hollands), but when bred to a true dwarf, they can produce showable, true dwarf babies. The does in particular can be useful because they have slightly larger litters, hardly ever have birthing problems, and never have peanuts. False dwarfs aren't just oversized, though; the dwarfing gene affects certain body parts in certain ways. The trick to successfully using false dwarfs in a breeding program is learning to recognize what good type looks like without the influence of the dwarfing gene.
On the other hand, if this female just has poor type, no matter how good her parents are, you would be dealing with conformation faults that might take many generations to weed out. You have to decide whether you want to work with that.
A litter of 5 week old blues and opals
The animal you currently have is an Otter, that's the Tan pattern. Blue is the Self pattern; breeding a Tan to a Self will produce Tans and maybe Selfs. All of the variations of Black-based and Chocolate-based (Black, Blue, Chocolate and Lilac) are showable in both Self and Tan patterns in the Mini Rex. If you want to play it safe, a Blue may not get you Chocolates, but it won't produce anything you can't show. Opal is the Agouti pattern. While you may not see them in the first generation, sooner or later, Chocolate and Agouti in the same breeding program will result in some whoops colors, some of which you may mistake for something showable, only to have the animal DQ'd by a sharp-eyed judge who knows what to look for (to the best of my knowledge, the only Chocolate-based Agouti-patterned colors that are showable in Mini Rex are Lynx, Tricolor and Red)