It's my understanding that Brazilian (and Portuguese) "middle names" are usually if not always family names, are they not?
Insisting that they are part of your surname sounds like it might be the easiest way to get it accepted - it is common enough in Europe to have surnames with spaces. E.g. a Dutch surname like "Van der Vaart", or "Van Helsing", so it's quite likely various agencies etc. run into that often enough.