Of course they will be sanctified through you because you are the influence. But they also have the freedom of choice. So you should not take for granted that you are Kingdom members, you still need to guide your children to the right way.
But we will respect their freedom of choice. Though our influence plays the biggest role in their choices but when they understand and come to the age of accountability, and can choose on their own (not because of you but because of their understanding of salvation) then they have to make their own choices and go through the processes of salvation. But it is going to be easier for them because you are already there.
And of course you, as parents, who are Kingdom Citizens, it should be very easy for you to influence your children to the Way of the Truth because the Word of God says, “Train up a child in a way which he shall go and when he is old he will not depart from it.” (Proverbs 22:6)
That is the influence of the parents in the Kingdom Nation of the Father.