If Brother's Keeper exports the name as you describe, it would appear to be the inadvertent culprit. Were it me, I'd simply change the file exported from Brother's Keeper from "(dot)ged" to "(dot)txt" and load it into Notepad. Use notepad's global replace tools to change all occurances of "/" to a space or "/ ". Save the gedcom with a new name and then see if that might look better on the website.
Suggest you also look closely at your database to see if notes and other fields wherein a slash can be found to see if they need be modified in some way.