I work in children's social work as a social worker, unless there are other issues than just not being able to cope, then it is highly unlikely she would get help from the social work department , as most departments are over stretched as it is with child protection, child welfare issues.
She could try home start, sure start, in scotland there is an organisation called working for families, ususually accessed throguh local nurseries, her health visitor will be better placed to advise on what is available in the area.