A rabbit really should have constant access to her actual cage (with its litter box). It isn't the type or appearance of the box that makes her go to it. It is because it is in a particular location (her cage) with her waste in it. Her chosen potty spot is in the cage in the litter box and she should have access to it at all times (and access to her cage as well). She's being deprived of that when she is in a run that has no access to her cage. (a secondary is box is fine too, but is best if it is in addition to access to her original box)
Rabbits get a measure of security by having the ability to retreat to their cage at will. It is their personal space, their safety zone, the place where they feel most secure. This is why it is helpful to allow a rabbit to have the option to retreat to her safety zone whenever she desires. Exercise areas should ideally be in the same place as the cage.
This also prevents one from having to physically pick up a rabbit and move him to or from his cage and exercise area. Regularly moving him typically results in a loss of that bond as bunny learns to resent being moved from place to place. The better option is to be able to just open the cage door to allow for exercise time. That way, bun can come and go as she pleases.
