Do I get this right? You cannot guarantee that each country code will only appear once your tables with (Country, Region) and (Country, Cluster) ...
If this is the case, you cannot add a new relationship between both tables, because there already exists one (through the Country table). Your problem would then be that filters applied on the Region Name would not automatically propagate to the other table.
One (tedious) solution would be to write your measures following the many-to-many patterns.
Probably better:
You could modify your main DB query to include the information from the other data sources (PowerPivot stores the data anyway, so it should not affect performance - only updates)
Otherwise, you can link both tables to your Country table (only through the Country Code column) and create calculated columns in the Country table using the LOOKUPVALUE function. The LOOKUPVALUE function may return an error, if a Country Code is associated with more than one Region or more than one Cluster. But in that case, you would have to take a second look at your data / model anyway.
Side note: I have a problem that carriage return no longer works on this forum (I must use Notepad instead). Is it only me?