Grandparents normally have no rights in respect of their grandchildren. They don't even have any right to know that they've got grandchildren. So your mother could have a long battle to try to change the situation. See this post for an example of someone who's trying to do something similar:
http://www.theanswerbank.co.uk/Law/Question352 688.html
(NB: Please follow the link, from that post, to the Grandparents' Association. They may well be able to advise your mother as to whether there's any point in contacting a solicitor).
However, irrespective of whether a contact order is sought or not, I strongly recommend that you or your mother should have a confidential word with someone from Social Services. It sounds as if they may already be aware of your sister's limited parenting skills, and the potential risks to her children, but it's easy for professionals to leave case notes sitting in a filing cabinet unless somebody takes the trouble to draw their attention to changing circumstances (such as the arrival of your sister's new partner).
Chris