Many of us make decisions on how to live our lives that our families don't approve of. Dealing with that in a considerate yet self confident way is an opportunity for growth.
I will draw a parallel with breastfeeding, since I am a lactation counselor. Many women I help get negative reactions from family members about their decision to breastfeed, or to continue breastfeeding for more than a few months.
There are several things you can say and do, to get nosy family members to butt out of your lifestyle, your way of loving.
1) Share information. Print off pages from poly websites or share a book about how polyamory works and how it is healthy for some people.
2) Use humor. (In breastfeeding, if someone asks, when seeing the mom and baby nursing, "How long are you going to do THAT?" say, "Oh, probably another 10 minutes or so.")
3) Express appreciation for their concern. This FM might love you and have a real fear you are being damaged by sharing love with more than one partner.
4) Be self confident. If you are happy and feel good about your life, show it! Don't allow them to rock you with their poison.
5) Do not allow them to castigate either of your partners. (Some people will mock a nursing toddler about how they are a big boy/girl and nursing is for babies.) This FM needs to back off your other partners.
6) Even though you say you are a private person, don't back down and hide your joy by not going out with your bfs. (Some women hide indoors to breastfeed, but the more women that hide it, the more of an oddity breastfeeding can seem when someone does nurse in public.) Go out, enjoy life, do it with pride!
7) Is what others have said. Draw clear boundaries. If you like this family member, tell them in no uncertain terms you will no longer discuss this topic with them, and continue your relationship with them. If they just won't back off, stop seeing them.
Remember, this FM might have cravings for other partners themself, and be projecting that longing onto you negatively.