But it was her relationship with the male neighbor that was especially upsetting to Mr. Jones.

“When asked his biggest fear, Mr. Jones stated that he did not want to feel abandoned by his wife,” Dr. Hames wrote. “He did not want to feel unwanted and ‘tossed away without even knowing it.’ ”

The two squabbled over who would care for the children and where they would live. Mr. Jones talked of moving his children to Mississippi, where many of his relatives reside, or relocating elsewhere in South Carolina, away from Mrs. Jones.

Their divorce became final in October 2013, and Mr. Jones, in an agreement with Mrs. Jones, became the custodial parent of the children.

Dr. Hames, whom Mr. Jones had hired, endorsed the approach in her affidavit.

“Mr. Jones is a highly intelligent, responsible father who is capable of caring for his children as the sole custodial parent,” she wrote, adding, “His thoughts are very detailed, action oriented and focused on his children.”

Last month, though, Mr. Jones was questioned by law enforcement officials about a report that he had physically abused at least one child on Aug. 7. The authorities said Wednesday that there were no signs of abuse when they visited the home that day and spoke to Mr. Jones and the children.

Amid the state’s inquiry, Mr. Jones and his children were living in a trailer home at the end of a sand-and-grass road here, part of a small community speckled with “no trespassing” notices. Residents described it as a transient neighborhood, with people rarely staying longer than a year or two and many inclined to keep to themselves.

Still, Mr. Jones and his family were not especially reclusive by the neighborhood’s standards. The children would often play outside — though they had been seen less and less in recent months — and Mr. Jones could be counted on for a wave or a greeting.