In a sense, your daughter is correct and so are you. Martyrdom is not to be sought out explicitly. Ecclesiastical history and traditions tell of how a lot of ‘zealous’ souls went to the lions in the arena… only for them to start banging on the doors as soon as the lions were shown. They sadly died in both states of physical and spiritual death.
There was the case of the Christero War a century ago. However, that was an extreme case and it was done with prudence and Charity on the Catholic side, but not so on the Secularist side. We know of only eight major battles fought (plus some skirmishes, but in all honesty, I don’t know enough Mexican history, sadly.) After a time, the Catholics won and the church bells rang again.
So, you are both essentially correct in a sense. We are to hide as we are called to preserve our lives. ‘Martyrdom must come from the heart, not from Rome’ as history tells us.
Bear in mind though: I am neither a theologian, or a scholar. I am just some poor, broke, dumb Catholic with an anxiety disorder that knows a thing or two, because I read articles, books, and such. Don’t just take my word for it. As scripture does indeed tell us: there is wisdom in many counselors’. Though, if I am wrong in this, please feel free to correct me and I will happily do so and accept.