It seems as though it possible your R4 card hasn't been updated to work on the latest DSi firmware
(I will warn you - It's possible that your R4 can't be updated, there's a lot of 'clones' that can't)
There should be a Web address on the flashcard (or box), I would suggest popping to the website & looking to see if there's a 'firmware update' (NOT a 'OS update') that you can install that will allow the card to work on the latest DSi/3DS Firmware versions
(BTW - you will need to use your Brothers DLIte to update the flashcard if an update exists)
FYI - Nintendo occasionally bring out firmware updates on the DSi and 3DS (DSLite and DSPhats are not affected) that 'block' flashcards & stop them from working.
It's usually a good idea that IF the DSi/3DS says there's an update avaliable, then DO NOT UPDATE until you check that a 'patch' is released for your particular flashcard (you can usually find a post on GBATemp that will help)