It means the person did not have a loving mother, but she has a desire to have a child of her own, but has fears of being like her own mother.

'Longing for a child' - The subject has a desire or wish to have a baby. that was matched only by her fears of "lacking the mother gene". - the subject, although having this desire to have a baby, is worried that she lacks the (inbuilt natural) ability to know how to raise (look after) a child. Hope that makes sense... :)