you can't arrest someone for telling a silly story or not crying enough. It's not evidence. Probably took a couple of weeks to process the body and analyze everything that was taken from it (apparently, bits of the coffee cup). Then to interview everyone they knew, go through correspondences, emails, etc. I don't know what the deal is with her alibi (that she was working that day) but anyone could have come in and killed him. And her strange behaviour and story could be due to mild dementia. You can't jump to conclusions.