Answer:
Well my mum is a neat freak too! One day I decided to confront my mum and actually tell her that I thought she may have OCD (Obsessive-compulsive disorder) which is an anxiety disorder. Symptoms of the disorder include excessive washing or cleaning; repeated checking; extreme hoarding; preoccupation with sexual, violent or religious thoughts; aversion to particular numbers; and nervous rituals, such as opening and closing a door a certain number of times before entering or leaving a room.
If you do not think your mum's case is this extreme then maybe you could help out by cleaning things or trying to help her, this may lessen the amount of 'neatness'/ cleanliness that she has to deal with.