Hi
Has your mother herself received a Carer's Assessment from social services?
http://www.nhs.uk/CarersDirect/guide/assessments/Pages/Carersassessments.aspx
"Most carers have a legal right to an assessment of their own needs. It is your chance to discuss with the social services department of your local authority what help you need with caring. You can discuss any help that would maintain your own health and balance caring with other aspects of your life, such as work and family. Social services uses the assessment to decide what help to provide."
If your mother can't cope with looking after your father yet they say he doesn't qualify for a care home place they have a duty to provide sufficent support to your mother to enable her to care for him at home - they can't have it both ways.
Does your father attend a Memory Clinic/Dementia service? It may be that you need to get a specialist in dementia care (ie if he's been seen by a psychiatrist or CPN via dementia/elderly services), to provide a report re the true extent of your father's problems and the inability of your mother to cope - social services are more likely to take notice of the opinion of another professional I'm afraid. It's a matter of continially chasing social services up - on a daily basis if necessary as they are exceedingly good at fobbing people off. You need to find out the name of the manager of the elderly services team and keep on at them. Whenever you phone social servies, ask for the full name fo the person you're speaking to, their job title and what team they work in. Then ask what they are going to do to help and ask by what date and hold them to it. You need to do this on behalf of your mother probably as it needs a lot of assertiveness and it sounds as if your mother is worn out from caring for your father.
Crossroads Care can provide a sitting service to give carers a break:-
http://www.crossroads.org.uk/?mid=21&pgid=141