I think "overlooked" implied he didn't notice them. This wasn't necessarily on purpose; he was just too busy to notice. Using "neglected" or "ignored" would implied that he knew his children had certain needs and he chose to ignore them.
Perhaps wait for other opinions on this. Personally, I would say that if he neglected the needs of his children he did not do that unknowingly. He knew they had needs, he noticed their needs, but he chose to neglect them.
I think that overlooked in this instance means that he was simply so busy with his work that he didn't have much time to spend with his children and deal with their needs and issues. Probably not intentional neglect. Neglect is a fairly strong word to use with regard to children. (Quickly brings into play social service agencies, in Canada). Ignored definitely implies intent.