Allowing your parent to be unhappy

I am very close with my younger sister and my Dad has expressed to both of us that he feels she doesn’t call enough, doesn’t return texts, and that is hurtful to him. He will even cry about it in front of us. She is working full time with 2 young children so I know that she is maxed out and isn’t available to be very interactive. I don’t take it personally when she doesn’t return texts right away because I know what it is like to have young children. I have explained this to him but he doesn’t seem to get it. I have a hard time just letting him be unhappy when I know it is based in faulty thinking. I think part of this is that I have always felt responsible for his happiness. How can I let him be miserable without taking it on?

Here is my model:

C: Dad doesn’t think Lisa calls enough and states he feels hurt by that
T: I can’t stand it that he is unhappy
F: Stressed
A: Ruminate about it, try to “fix” him
R: I take on his unhappiness