I was searching for Hugo H. Tidball (Sr.)'s date of death and found your link.
You have actually mixed Sr.'s and Jr.'s wives.The first listing you have for the 1900 census with Hugo H. and Hattie is Hugo Jr. (Jr. born in 1845).Hattie is Jr.'s 2nd wife and her name was Hattie E. WARD.
The second listing you have for the 1870 Ionia census is for Hugo Sr. (born abt 1821) and his wife, Fanny M. COLEGROVE.
The last listing you have for the 1880 Cook, Illinois census is for Hugh Jr. and his first wife, J. Emma (1846-1896).It doesn't look like Hugo Jr. waited too long after Emma's death to marry Hattie.
I would like to add some additional information in case someone else finds your posting.
After looking at various information, I believe that the Lincoln listed on the 1870 census living with Hugo Sr. and Hugo Jr. is the son of Hugo Jr. and J. Emma Tidball and NOT the son of Hugo Sr. and Fanny.
I believe this is supported by the fact that the son of Hugo Jr. and J. Emma is listed as Abraham L. Tidball born in Mar 1865 and yet NO Abraham appears on the 1870 census with Hugo Jr. and J. Emma.However, there is a Lincoln listed below Hugo Jr. and J. Emma on the 1870 census and he was born in 1865.
In 1880, there is a 15-year old Lincoln living with Hugo Sr. and wife, Fanny, yet there is NO 15-year old male (Abraham or other) living with Hugo Jr. and his wife, J. Emma.I believe this supports the assumption that Lincoln Tidball b. 1865 and Abraham L. Tidball b. 1865 are one and the same.I think Abraham/Lincoln was staying with his grandparents for some reason.
Thanks for taking the time to put all this information online!