Have you looked at Daniel's marriage record, which might give parents' names and county of origin?
Have you looked at death records for the Mulcahys, which might give parents' names and county of origin?
Have you found their obituaries/death notices? They sometimes include place of origin in Ireland.
Have you looked at probate records?
If you haven't, it's a good idea to look at all the available U.S. records before going to the Irish ones.
I hope this is helpful.