Betty...I see what the Keith book has to say, now here is the All Leatherman Kin Book, pge. 244.
Cora Alice Keith, b Auglaize twp, Allen Co., OH July 24, 1879, m 1st, Bear Lake, Manistee Co., MI, July 3, 1902, Alfred Leas, b Preble Co., OH, May 23, 1849, d Brethren, MI, April 14, 1911; m 2nd Brethren, MI, Oct 20, 1912, Charles F. Carlson, b Sweden, July 31, 1873, d Brethren, MI, Jan 14, 1919; m 3rd by Charles N. Dickens, magistrate, Grand Haven, Ottawa Co., MI, Jan 20, 1920, William Cross, b Ypsilanti, MI, Nov 22, 1859.Children: Arthur; 1st m, Alma, Charles, Lillian, John; 2nd m, Carl; 3rd m, no issue.
Your info says there was a child named Cross from the 3rd marriage that doesn't show in the ALK book. It does however show, as you can see above a child named Arthur. This child is listed as Arthur Keith.Perhaps a child out of wedlock, as it seems to indicate.There is no other info on him other than posting the name.I am showing the progenitors of the Hill/Keith connection as the marriage of Elenore Hill b PA in 1825 who married John H. Keith, b 1825 in Allen Co.I think the Keith book has all this, but if you need any of that info, please contact me....firstname.lastname@example.org