The book I am looking for is a children’s book that I had when I was about 5 or so and I am now 40.

The book is about an old big cat that would sit with its owners baby girl and push her in a swing daily and the baby loved it.  Then one day the baby girl’s mom sent the cat to go live somewhere else (I think that the cat went to a farm, it was not a huge part of the story at all, so I am saying a farm, it could have been somewhere else, the cat was definitely sent somewhere)  The baby would not stop crying for the old big cat.  Nothing calmed the little baby girl down.  So the mom got the cat back.  And the baby was happy again.

The front cover of the book is a cat pushing a baby in a swing.

It is a hard cover book.

I think the title may have been the cats name or the name the baby girl called the cat

I appreciate your help with this, I have been trying to remember the name of this book for a long time so figured I would try this way out.