SueBee47 You are in a desperate situation, but I am a little unclear of the ins and outs so I hope you do not mind if I try to summarise your situation.
Your daughter has sadly led an unsettled and unstable life and has three children, all with different fathers. She is currently in a relationship with a physically and mentally abusive man.
Your three GC are 1) a 10 year old boy who has lived with you since birth, 2) a 6 year old boy who spend most of his time with you and, presumably gets on well with his brother, 3) a 3 year old girl, who you do not know well because of your health problems when she was born and the fact that your daughters behaviour had driven you to breaking point at that time. This child has spent her whole life with her mother and been the 24/7 victim of the abusive household she has lived in and is herself, clearly very disturbed.
Of your grandchildren, she is the one who needs you most. None of what has happened to her is her fault. She did not ask to be born or live in such dire circumstances nor did she do anything to assist her parents in making her so disturbed. She is the entirely innocent victim of your daughter and her partners.
If you possibly can, and I can understand why you are thinking twice about taking on all three children, with one clearly very disturbed, take all three, but negotiate very hard with Social Services over the conditions. Your little grand daughter should be in nursery that can cope with her very special needs at this point. It should operate all year, not just during school terms so that during the holidays the boys have a time at home with you without her. Few boys of 10 and 6 have any interest in sisters aged 3, but only have her in nursery 4 days a week, so that in school terms you can give her your entire attention for one day to get to know her, have compassion for her situation and, hopefully, come to love her. In the holidays it will help her brothers adjust to having her around.
However do get some help and support for yourself. Contact the Family Rights Group www.frg.org.uk/ They have an advice line and can offer help and support in dealing with Social Services and yourself.