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/0743428641

http://ocslha.com/Ferre.htm

http://www.fldoe.org/ese/pdf/y2001-9.pdf

Hope this helps!