There is abundant evidence that if you were maltreated as a child you are more likely to become a maltreating parent, but there is less evidence that good care results in good subsequent parenting.
A study published in Child Development observed 200 parents interacting with their three-year-old children.
All of the parents had themselves taken part in a study which followed them from birth. How the mothers had been treated in early childhood, middle childhood and adolescence each predicted whether they were warm, sensitive and stimulating themselves with their three-year-old. Implication: how you are caring for your child will affect how your child cares for your grandchildren.
It has often been claimed that what a child is like when it is born significantly determines how it is looked after, although most studies show this to be false: a newborn child's personality (reactive-passive, irritable-calm, etc) does not predict what it is like at three months or subsequently, whereas how it is cared for does.
A study (in the Journal of Child Psychology and Psychiatry) of parents of five-month-old twins also found that infant personality did not affect parenting. Parents' views of how good they were at calming the child, how good they were as parents and how protective they were, were unaffected by the child's innate behaviour. Implication: beware of books that blame Little Jimmy's inborn character for his love of pulling the wings off butterflies.