There are several factors to consider in answering this question.
Are the twins in the family a result of fertility treatments? These treatments include fertility drugs and assisted reproductive technologies such as in vitro fertilization. The use of such fertility treatments has caused a skyrocketing in the number of fraternal (dizygotic or DZ) twin births (and also higher multiple births). But this does not increase the chances of other family members to have twins.
What kind of twins are in the family? It was believed that identical (monozygotic or MZ) twins occur at random. There is now some evidence to suggest that MZ twinning may run in families, but this is very rare. On the other hand, DZ twins are known to run in some families. DZ twins occur when two eggs are released at the same time and are fertilized by two different sperm. It is believed that there are genetic factors that can cause hyperovulation, which is the release of multiple eggs during ovulation. These genetic factors have not been identified and there is no genetic testing available for them.
On which side of the family are the twins? If DZ twins are on the wife’s side of the family, there is a chance that a genetic factor for hyperovulation runs in the family and that the wife has inherited it. If so, the couple may have an increased chance of having DZ twins. If DZ twins are on the husband’s side of the family, this does not increase the chances that the couple will have DZ twins. However, if the husband inherited a genetic factor for hyperovulation, he could pass it on to his daughter(s). That could increase the chance that the couple will have DZ twin grandchildren!
Factors such as maternal age, race, weight and diet all contribute to twinning. Such factors may have a stronger influence on twinning than family history. This is discussed in the answer to the question “What factors are related to DZ twinning?”