I think I read this at one of my grandparents in the early 1980s, but unfortunately, many of those books have been lost over the years between sticky-fingered grandchildren, general wear and tear, and my surviving grandparents trying to reduce their footprint. I want to say it was two books, probably under 50 pages, hardback, both by the same author. It was a series of misheard phrases in the form of sentences, sometimes a single page and sometimes a two page spread, over a beautiful illustration (I want to say watercolors) of what a child might think they hear. Ones that have stuck with me over the year was one with the mother having a "frog in her throat", showing said frog peeking its head out of her mouth, one where they talk about their family having a "coat of arms" with the illustration showing them opening a closet with a coat covered in arms. There were at least two entries involving a confusion between "prince" and "prints", one involving a "blue prince", one with the "foot prince in the snow". I know there were more, but those are the ones that are coming to mind.
And, of course, right after I post my question, a few further searches found the books. The King who Rained and A Chocolate Moose for Dinner by Fred Gwynne are the books I was looking for. The key came when I started searching for combinations of the phrases I remembered and came upon this page which was discussing using it for a lesson plan on homonyms.
Phrases from the book: (Will be in a handout)
A king who rained for forty years
Forks in the road
A mole on his nose
Lambs gamble on the lawn
A frog in her throat
A little hoarse
I’m a little deer
Hold up her train
A head on beer
Coat of Arms
Live in the present
Foot Prince in the snow
Blue Prince for the new room of our house
Boars coming to dinner
They didn't mention the title of the book, but I tried the first term and that brought me to a page on Gwynne's book.