So far, I have found no direct evidence identifying the parents of Joseph Haws, G2-grandfather of Harold Hawes. According to The Household Guide and Instructor, with Biographies, History of Guernsey County, Ohio, with Illustrations by T.F. Williams, Joseph was born in Maryland, and lived with his wife, Ann Galloway, in Montgomery County. This is the furthest back direct evidence of our Hawes ancestry goes.
Some family trees on the internet list Joseph's parents as Michael and Rachel Haws, but no direct evidence is provided. Assuming the book above is accurate, evidence suggests it is likely that these were indeed his parents, particularly given there are seemingly no other adult Haws/Hawes/Hawse in Montgomery County, Maryland in the same time period when Joseph would have been a youth. Below is a list of evidence:
There is a Michael Hawes listed in "Montgomery County, Maryland Oaths of Loyalty" from 1778. NOTE: This is the only time until the late 1800s where the spelling is "Hawes". [Source: http://genealogytrails.com/mary/montgomery/loyalty_oaths.html]
The "1790 Montgomery Co., Maryland Federal Census" on USGenWeb for Michael Hawse shows 2 males 16 and over, 2 males under 16 (Joseph would have been 8/9), and 5 females. The same data is seen at FamilySearch (source of the image below). [Sources: http://usgwcensus.org/cenfiles/md/montgomery/1790/pg00091.txt, https://familysearch.org/ark:/61903/1:1:XHKY-W44]
In the 1810 census, there is a Rachel Haws in Montgomery County with 1 male 16-26, 1 female 26-45, and 1 female 45+. Presumably Michael had passed away by this time. [Source: http://us-census.org/pub/usgenweb/census/md/montgomery/1810/pgs-301-to-370.txt]
The only other mention of a "Haws/Hawse" in Montgomery County I have found in the timeframe 1780-1800 is a marriage of Rosanna Hawse to Sylvester Sullivan on 5 Aug 1797. Since there were 5 females mentioned in the 1790 census, this is likely a daughter of Michael. [Source: http://genealogytrails.com/mary/montgomery/marr17951798.html]
Joseph Haws married Ann Galloway in Montgomery County. In researching, there are occurrences of Galloways both in Montgomery County, and also in Belmont County and Guernsey County, Ohio. The families likely migrated to Ohio around the same time.
There are a few pieces of evidence that suggest the families knew each other well:
In Early Ohio Settlers: Purchasers of Land in East and East Central Ohio, 1800-1840 (p. 127), there are two entries of land purchases that may be Ann, 1 of which is with a Galloway that may be her father or brother: Haws & Galloway (Z-M), 6 Jul 1830, Guernsey Co., Ohio (03 01 24); Haws, Ann (Z-M), 12 Jun 1829, Belmont Co., Ohio (03 01 25).
Ann's brother Elijah signed the marriage license for John Haws and Hester Perkins. See Hawes is Haws.
A Benjamin Galloway witnessed the marriage of Rachel Haws, Ann's daughter, to Landon Heskett. This was likely Ann's father, Rachel's grandfather.