Custom aggregation for non-leaf level nodes to avoid double counting
The right approach for the problem is to use many to many relationship in SSAS.

More details here https://stackoverflow.com/questions/10971593/custom-aggregation-for-non-leaf-level-nodes-to-avoid-double-counting and here http://www.sqlbi.com/wp-content/uploads/The_Many-to-Many_Revolution_2.0.pdf. 

Then no MDX is required.