I think I would have my "banana ice cream", which by the way, I find delicious and refreshing, and opt out of going with the family. If they're just going to the ice cream shop and back, you don't miss much, and it might actually be a point of decision-making for the rest of the family.
Sometimes families develop unhealthy food habits and you have to decide what you are willing to do or not willing to do.
When I was a teen, I stopped eating desserts. I ate three meals a day, sometimes, snacks, but refused to eat desserts. This bothered my mother tremendously, to the point where one time she actually ordered an ice cream for me at an ice cream shop and expected me to eat it. But by taking a position and just keeping my resolve, I was able to keep my weight down in my teens.
Who knows? They may give up their habit or change to another healthier one (like a walk in the neighborhood or at the park) as a result of your opting out.
The most effective health-care is self-care.
Nutrition is the prescription.
You can literally stretch your lifespan by shrinking your waistline.
Nutrition and other lifestyle factors that you can choose are a more significant determinant of your health than genetics.
Filling your stomach with high-nutrient foods is like by-pass surgery without the surgery.
We are all born with an innate desire to not only survive but thrive.