First of all, if there's no actual invite yet, don't even worry about it. I'm giving some serious side-eye to your relatives who are giving you agita and trying to make you "choose sides" about a *possible* date conflict based on a rumor.
Even more side-eye that they are trying to make you rank your relationship with this bride in comparison with siblings. So it's not just a loyalty test of friends vs family, but comparison among family members?
Sorry, but your relatives kinda suck.
If the family invite materializes in a reasonable notice period (as pp said, a month out, not a week out), and if you personally feel that attending the family wedding is more important *to you* than the friend wedding, then I think your friend would probably understand.
If it's too close or you just don't want to change, then you unfortunately have a prior commitment and you do *not* need to explain what it is. Honestly, if your relative is getting invites out on very short notice, they can't expect everyone to make it. People book trips. And surgery. And all kinds of things. It's just life.