I don't know with certainty that one has a dominant ear - but I know we have a dominant eye - so it stands to reason our ears would work in a similar fashion. Taking the behaviors you describe, the dysgraphia and other speech and language issues together, it seems that CAPD is a possibility.
Here are a couple of resources you may find helpful:
"When the Brain Can't Hear"
http://www.amazon.com/When-Brain-Cant-Hear-Unraveling/dp/0743428641http://ocslha.com/Ferre.htmhttp://www.fldoe.org/ese/pdf/y2001-9.pdfHope this helps!