The answer here is no. Having a mother, sister or other female relative deliver a baby prematurely does not mean that you will too. Most of the reasons for a premature delivery are not genetic and include problems with your placenta (premature separation), an over-distended uterus (too much amniotic fluid, twins, triplets), drug use, smoking and certain bacterial infections. Additionally, many times we can't find a reason for why someone goes into preterm labor.
So it is certainly worth mentioning to your practitioner, but rest assured, there is not a "preterm labor gene" that your mom could have passed to you.