Your probably correct concerning George Appleman. There's only one curious issue. My father told me that back in the day when William Appleman was around, if anybody asked him about his father he would get extremely upset and tell that person to never ask him about his father ever again. All his children and relatives were told to never ask him about his father. When his mother died, he was only 18. His brother Henry was only 16. If their father was still around and wanted to live with him instead of the Waite family and he said no for any reason, that could have created bad feelings. Henry Appleman is listed on the 1894 census as Richard Waite's Step-son. Maybe Richard adopted Henry after his mother died so he had someplace to live.
You did point out somebody I didn't now about, Tina Waite in the 1910 census. That shows that Henry considered the Waite family as his own. I wonder if Tina Waite is one of Richard Waite's brother William's kids. He had a big family. Many of them died young.
If William had a relationship with his father George through the late 1880' and early 1890's up to his marriage to Anna Bishop, I don't know how to confirm that. William and Anna's only child, Roy(my grandfather) was born in Put-in-Bay Ohio. I don't know why they were there for a short time. All of Anna's family also lived in Attica.
You say you're not related to any member of my family. What sparked your interest in my story?
I have another member if my family that discovered the same road blocks about 20 years ago doing all this the old fashion way. She's my fathers cousin. We comparied notes after I put my family tree together and most of it came out the same. I discovered a few more details. I favorite document are the Marriage registry's. They confirm parents names. Thanks for your input.