Abso-fucking-lutely they should...
I don't like the idea of a potentially world ending nuclear stand-off, but we've learned well enough from these past couple of years that having nukes is the only way to guarantee your country's sovereignty against other nuclear powers.
Honestly I get your frustration. Feeling like you're being hidden away...
But I think you're taking what you've got for granted. It sounds like your family is fairly liberal and well-meaning, but that doesn't mean her's is.
Even in the west, religious conservatism can get nasty real quick (especially for woman), so I can absolutely see why she might be scared to tell her family.
She probably doesn't like hiding you in the shadows any more than you do - you should be careful putting your feelings over her well-being.