If we distribute our software both GPL and under a commercial license, do we have the right to incorporate third party patches into the commercial version of our software?
It depends on the terms under which the patches were conveyed to you. If they were conveyed under, say, a modified-BSD (or other weak copyleft) licence, then yes, you may. If they were conveyed under GPL or another strong copyleft licence, then no, you may not. If the copyright was assigned to you, then you may distribute them under any terms you choose.
So you'll have to ask the author of the patches what he or she intended, assuming (s)he has not already made this clear. And, of course, IANAL/IANYL.