Libertarianism isn't actually about the level of government power as it is about the scope of government action.
For instance, our current society might be very lax when it comes to enforcing laws against tresspassing, fraud, and violent crime. A government that enforces these things extremely severely, but also has no drug laws and has privatized roads and utilities, might have "more power" in some absolute sense but still be more within the scope of libertarian ideals.
The OP happened to touch on one of the areas where I believe a libertarian government still has the right to interfere greatly, which is to say the protection of minor children (and, to go further, the production of those children).
A libertarian government isn't necessarily "less" government than today. It's just that today's government is involved in so many areas that libertarians find impermissable, that reducing government interference in those areas is the primary thrust of a lot of libertarian thought and action.