Ensuring kids' safety in a household with guns
For anyone who overrides self-preservation impulses out of fear of appearing rude, "The Gift of Fear" and "Protecting the Gift" by Gavin de Becker are required reading -- since I doubt you'd literally rather die than offend.
My brother and new sister-in-law are very religious, not to mention very conservative. My boyfriend and I are agnostic and progressive. However, I was raised in a very religious household, and growing up I attended church every Sunday and wasn't allowed to miss unless I was ill. At 18, I decided organized religion was not for me and have not been inside a church since, except for a wedding or funeral.
Whenever we go out as a family, my brother and sister-in-law insist on praying out loud, whether we are in public or at home. When my mother is there, I indulge the practice, but when it's just the four of us, I prefer not to and I am uncomfortable when this occurs. I have asked twice if we could all just say a private prayer to ourselves rather than have a group prayer, but I'm overruled.
I feel strongly that I shouldn't have to partake in their prayer ritual. How should I address this?
You shouldn't have to partake in their prayer ritual.
And they shouldn't have to partake in your moment-of-silence ritual.
So you have in fact addressed this: You suggested saying a private, silent prayer instead of a group one.
Your brother and sister-in-law simply overruled you, as they had every right to do. Likewise, you have every right to opt out of the group prayer and remain silent as you prefer.