From a 2012 Bill Murray Interview in Esquire comes this:
If you bite on everything they throw at you, they will grind you down. You have to ignore a certain amount of stuff. The thing I keep saying to them lately is: “I have to love you, and I have the right to ignore you.” When my kids ask what I want for my birthday or Christmas or whatever, I use the same answer my father did: “Peace and quiet.” That was never a satisfactory answer to me as a kid — I wanted an answer like “A pipe.” But now I see the wisdom of it: All I want is you at your best — you making this an easier home to live in, you thinking of others.
There are stages in parenthood when your children occupy all of your mental time, and when they do, you may find your mind is closed. If before parenthood you found yourself open to contemplate and examine ideas, after parenthood you may find that your ability to do that has shutdown. I found that for certain stages of the life of my child, all of my time was spent either focusing on their care or worrying about them. But then there were stages when they settled down and there was less to worry about and my mind freed up again.
If you are a parent and you find yourself wrapped up in the state of your child, you should believe that that will pass, and while you never stop thinking about them, you will find you think / worry about them less. This is a good thing.