Normal. I have said it before but I think the parent-child relationship is unique in that in other relationships, the longer you know someone the more you get to know them and the deeper/closer your love/relationship is. With children it cannot be this way. The whole universe is puling them away from us so that they can lead their own lives. But this is how it is meant to be. As Kahlil Gibram wrote:

Your children are not your children.
They are the sons and daughters of Life's longing for itself.
They come through you but not from you,
And though they are with you yet they belong not to you.

You may give them your love but not your thoughts,
For they have their own thoughts.
You may house their bodies but not their souls,
For their souls dwell in the house of tomorrow,
which you cannot visit, not even in your dreams.
You may strive to be like them,
but seek not to make them like you.
For life goes not backward nor tarries with yesterday.

You are the bows from which your children
as living arrows are sent forth.
The archer sees the mark upon the path of the infinite,
and He bends you with His might
that His arrows may go swift and far.
Let your bending in the archer's hand be for gladness;
For even as He loves the arrow that flies,
so He loves also the bow that is stable.
Enjoy the bitter sweetness of being a parent