The children of Benjamin Applegate and Rebecca Wall are pretty well researched and known.People have been working on the big Applegate tree for about a hundred years now.I'm just the latest one trying to fill in the citation blanks and solve the remaining mysteries.
I found a marriage record for "Peline" Applegate and Robert E Craighead at familysearch.org.
I have transcripts of part of the messy guardianship file for the younger children of Benjamin.It was messy because he had set up to have his son Abraham be the guardian for his younger siblings, but Abraham died in the Mexican American war and wrecked the plan.
Benjamin died in 1845.His widow Rebecca and the younger children are in the 1850 census for Brown Co., OH.You can get an image of the page at familysearch.org
As to William Craighead--looking more closely at my stuff, it turns out a William Craighead married Pauline's older sister Rhoda (b. 1818).William was born in about 1817 in Ohio.Rhoda and William were living with their children in Scott Township, Brown Co., OH.William was a merchant.By 1870, William was gone, but Rhoda was still living in Scott Township, age 53, keeping house with Flora age 15 and Emma age 13.So the William could be the brother-in-law.