Human beings are social creatures, it is very normal for you to fear rejection by your family. No doubt your choices will have an effect on them, but it might not be a negative one. I for one got much closer to my family aftrr starting transition.
The best advice I can give you is just be honest but firm, tell your therapist, family, etc how you feel and if it is serious to you don't let them take it trivially. There is no need to hurt yourself or damage tissue you might want to repurpose in the future to show people how important it is to you, it might be difficult but words and less dramatic actions can convey your sentiments just as well.