I do not have kids yet, but I am pregnant and due in September. I also have a good number of parent friends, anarchist and not, and spend some significant time with my "godkids".
I think this question is about the problem of how do we live as anarchists in a not anarchist world, or what does that practice of an impossible idea look like.
Often the response to this line of inquiry is that people want to choose how they interact with themselves, others, and the society around them. Freedom, in this sense, is defined by understanding oneself, ones friends, and ones enemies well enough to make informed decisions about how to live and who to be. In my opinion that requires insight, strength, long-term thinking, ethics, patience, critical reasoning, manipulation/strategy, resilience, and versatility.
My goal is to best provide my child(ren) with the above skills so they can be agents in the world, not targets, to whatever extent possible. I do not believe that pretending the authority/power/heirarchy that is inherent in a parent child relationship does not exist will do that for them, I think it is dishonest, confusing, and a disservice to us both.
Freedom isn't something I will give my children by a lack of structure, authority, or discipline. I often find that the less structure and discipline I have the more trapped and overwhelmed I become, the more I am a victim of an emotional state produced in part by a terrible world. My kids feelings are only so important - I want to give them the tools to identify their feelings, experience them, and then decide how to act on them or not. That process takes time, and it takes years of me modeling that behavior as well as helping them acquire it by not letting them do what they want and feel all the time. Freedom isn't something I will give my children by thinking that I can protect them or remove them from this world (public school, media, bedtimes, loneliness), it is something I will give them by teaching them how to interact with those things so that they get the most out of them and so they can be critical of them instead of criticized by them.
My kids need me to survive and they need me to treat them developmentally appropriately, and that will be changing as fast as they do, and I am excited to talk about life in a million different ways as time goes by.