Remember, Linda is very convincing. I think that when Linda and the boys were first interviewed they appeared to be an intact, loving family. It would seem that she had no motive for killing him. My guess is that the detective initially believed her but after putting more and more clues together he eventually became convinced of her guilt. Also remember that Patrick was non LEO working for the Sheriff's Dept. All those LEO seemed to have no suspicions either and spoke highly of Linda. If I recall correctly, some anonymous letters to the editors appeared in the local paper inquiring as to why she was not being charged for murder and why she wasn’t in jail. I also saw some internet documentation from the insurance company refusing to pay off until a further investigation was initiated. Possibly external pressure caused a further look. From my point of view though, the investigation really hit high gear after the first jury hung.
My co-workers and I, including Linda, would chair Inter-Disciplinarian meeting which could sometimes get a bit dicey. Generally though, no big deal and you just get through it. I recall that Linda had a fainting episode in one of her meetings. Paramedics were called, fire engine, police, Program Director, etc arrived. Much drama. Meeting canceled. Out of literally hundreds of meetings that we all chaired, Linda was the only one who ever fainted for no particular reason. Just saying she might have had some practice for the sentencing!