The "Twin Gene" is actually a genetic predisposition to Hyper Ovulation. Hyper ovulation is when a woman's body has the tendency to release multiple eggs during ovulation, leading to fraternal twins.
It is possible that you have inherited the gene for hyper ovulation, making your chances of having fraternal twins higher.
The chances of having identical twins, on the other hand, do not seem to be genetic; So, the fact that your BF is an identical twin does not likely affect your chances of having twins. Fertility treatment can also increase your chances of having multiples.
Depending on when your mother was pregnant with you, the doctor may not have had access to ultrasound technology that is used today to diagnose twins. He likely had only measurements and touch to diagnose twins. Conditions such as a high amount of amniotic fluid around the baby can account for larger measurements; That, coupled with a family record of fraternal twins, could have led the doctor to believe that your mother was also carrying twins.
Thank you for the great questions! I'll look into writing an article on this topic.