I think you need to substitute the word 'real' with 'ideal' on SD's behalf.

ETA: Starting in the 1930's, scientist Harry Harlow did a lot of studies involving rhesus monkeys trying to investigate the mother-child bond. These studies are now considered very controversial due to how the monkeys were treated. But a lot was learned about what was needed to form a bond.

The monkeys were given two 'mothers', one warm and soft, the other which was made of wire and provided food. In all cases, the monkeys would run over to the food 'mother' to eat and then run back and cling to the soft and warm 'mother.' This experiment revolutionized American society.

Adoptive parents learned that they could form a 'real' bond with their children, even though it was previously thought this was impossible due to the lack of breastfeeding.

All parents learned that they could form a 'real' bond with their children, even if the child went to daycare or was otherwise substantially in the care of someone else.

***So my message to you with that information is this: Don't do more for SD than you are truly comfortable with, because the doing and the (love) connection/bond are different. And that it is possible to have a warm and loving bond.

On another note, read this article: http://www.examiner.com/article/how-children-deal-with-abuse I've paraphrased below.

Children naturally idealize their mothers and fathers and in effect view them as all good, all knowing, and incapable of being or doing any wrong. Idealization is not unique to children. Adults will often idealize their romantic partners, at least initially, and only see their positive qualities while ignoring the negative ones.
However, for children this process is not an option, it is an essential part of being an infant or a young child. It certainly does not last forever, the closer that a child gets to adolescence the less idealizing he does and the more critical, rebellious, and independent he will become.

Under ideal circumstances when a child is given the proper parental attention, affection, and validation the process of idealization works to the child’s benefit both in the short and in the long-term. However, what happens when a child does not grow up in the ideal circumstances? What if a parent is verbally, emotionally, or physically abusive, will the child still idealize the parent? Unfortunately, the answer is YES.

In fact the more abusive the parent is the more the child feels the need to idealize them.

So your SD is walking around with this crap in her heart, and you're living with it. I don't remember how old your SD is, but the more she can lose her shame and dependency about her BM, the more she can be 'normal'.

Thankfully, my skids NEVER mention their mother. Even when Medusa was in the picture, I think they just said "mom"....

she hasn't laid eyes on them in almost 4 years...