Hello, I'm wondering if the book your mom remembers could be "Lucky Mrs. Ticklefeather", a Little Golden Book published in 195l. She had an exotic bird, a puffin named Paul. She was "a very thin old lady", who "lived on the top floor of a high, high, terribly high building" in a big city. The puffin disappeared one morning (he'd gone to go find his dear Mrs. T. a sunflower she had wished for to put in a big vase she had). She called the police, and a policeman set out to find the puffin, who had run into trouble and was in danger of becoming Mr. Macaroni's dinner. The policeman saved Paul and brought him back to Mrs. Ticklefeather, with the sunflower he'd found for her. The author is Dorothy Kunhardt, Little Golden Book #122. The story is also in a larger book, a treasury of Dorothy Kunhardt stories. Most copies I've seen online are very pricey ($30 to over $100), but there's one of the D. Kunhardt treasury storybooks on Amazon for only $12.94/$3.99 shipping. There's many other good used-book websites you could check also. I don't know if this is the story your mom is remembering, but I hope this helps you in your search. I have a copy of the book if you have any more questions about story quotes, illustrations, etc., that might jog your mom's memory. I've done many book searches of my own, and I'm always glad to help others in their quests!
It was a book my mother read as a child (she was born in 1945) and it's a book about a woman who has an exotic animal -- an elephant or a hippo or a rhinoceros, something like that -- and brings it to her neighborhood. The story tells of all the crazy things that occur because of it.
I'm pretty certain it has Mrs in the title but that's not definite.
Any help would be great!