I have been researching the Joseph S. and Richard T. McAndrew families that went to Lawrence Co.,MO in 1850 as myline descends from Richard and Sarah through their son John W. McAndrew and I never found a John Joseph McAndrew.
The 1870 census lists both families as living in Green Twp,Lawrence with children of Joseph and Melinda as:
William 14 Elizabeth 8 Susannah 7 Perry5 John H.3 George W. 1
I believe the John H. is John Hugh and not John Joseph also it appears that William is the son of Joseph and Elizabeth and the remaining children are from Melinda. Do you have any more information on their kids, such as marriage and death?