at crabby's post.
I'm a rabid liberal leftie BTW
I'm also a single mother who left my twins' father when they were 4 months old. They have had none of the problems associated with so-called broken families, and I would say that my 'family' was broken when I was with their father and became rapidly fixed once I left him. They are no longer exposed to his abuse of me nor his questionable values and morals.
IMO far more damage is done by people clinging to relationships that are highly dysfunctional and sometimes abusive than is ever done by a mother deciding enough is enough and leaving. The short-term upheaval may have a detrimental effect but it passes and the long-term stability that follows more than undoes the damage.
OP your 3-year-old will probably be fine in time. The Children's Society report and loads of other research shows that the long-term outcome for a child from separated parents is most affected by the child's relationship with the main carer (which is why they recommend single parents NOT be forced into work in the 12 months immediately following a split, so that they can concentrate on strengthening the relationship and dealing with any insecurities about the new way of life). The other factors that most influence children's outcomes are the primary carer's level of income and education. In fact, the poor outcomes for children from single parent families that we are always hearing about become statistically insignificant once you remove financial inequality from the picture - suggesting that money is far more influential than the relationship status of the parents.
If your DD has an otherwise positive relationship with her father, take comfort from the fact that research suggests that the quality of the relationship with the non-resident parent seems to be more important than the frequency of contact (see Dunn, 2005).
IMO as long as you love your child, do your best and provide a stable home life from this point on, your DD will be equally as fine as your twins. 