Do twins "run in the family"?
The propensity for heterozygotic twins seems to be driven primarily by genetics, with additional factors playing a role (http://152.98.160.29/contents/p/staff/CV162Lewis_UQ_Copy.pdf', info site):


hormones ("Mothers of fraternal twins tend to be taller, and have earlier and shorter menstrual cycles")
ethnic background (which is really genetic) - African women are more likely than Caucasian women to have them, and Caucasian women are more likely than Asian women to have fraternal twins
mother's age
nutrition
previous births
fertility drugs


I also found a link to a genetic study published in Nature that claims to have linked a DNA region to dyzotic twins, but the Nature website seems to be down - maybe it will work later: A region on chromosome 3 is linked to dizygotic twinning - Nature.

Note that the father does not contribute to the chance of having heterozygotic twins, but a male offspring could pass the gene to daughter.