It's a bit of a stretch, but I wonder if you're thinking of the story “Light Verse” by Asimov. I read it in Buy Jupiter but it has also been anthologised elsewhere. It wasn't pubished in Analog.
The old woman is the owner of a robot, Max, that was defective when delivered to her:
The very last person anyone would expect to be a murderer was Mrs. Avis Lardner. Widow of the great astronaut-martyr, she was a philanthropist, an art collector, a hostess extraordinary, and, everyone agreed, an artistic genius. But above all, she was the gentlest and kindest human being one could imagine.
She is famous for her light sculptures. The link to poetry is in the title and the line in the story:
“I wouldn't call it 'poetry in light.' That's far too kind. At most, I would say it was mere 'light verse.'“ And everyone smiled at her gentle wit.
The robot creates the light sculptures. Although the manufacturing fault means it isn't much use for everyday tasks, it somehow endowed the robot with the creative genius to make the sculptures. I won't give away the ending in case you want to reread it.
The story doesn't match the description of the robot replying to questions about military issues or space travel, but it matches in enough areas that I wonder if it's being conflated with another story in your Dad's memory.