I was thinking about this myself, after just having watched the film for the first time in decades. The answer, to me, was quite simple. Give up the MGM-think! Stop worrying so much about the plot! She could simply have been a guest at the hotel, who Groucho has a couple unrelated-to-the-plot encounters with. In the same manner as the delightful scene where Groucho won't let the old couple into the hotel without a marriage license wonderful fun and yet has nothing to do with the plot. A nice touch might have been to name her Mrs. Potter implying that she was actually the same character from "The Coconuts", now living in a different hotel.
An excellent idea! Too bad they didn't think of it at the time.

I was thinking about this myself, after just having watched the film for the first time in decades. The answer, to me, was quite simple. Give up the MGM-think! Stop worrying so much about the plot! She could simply have been a guest at the hotel, who Groucho has a couple unrelated-to-the-plot encounters with. In the same manner as the delightful scene where Groucho won't let the old couple into the hotel without a marriage license wonderful fun and yet has nothing to do with the plot. A nice touch might have been to name her Mrs. Potter implying that she was actually the same character from "The Coconuts", now living in a different hotel.

True. but where would you put her in the script.
She couldnt be the Beauty.she couldnt be the young officers girlfriend.
The script would have to have her part written in and by then Groucho wasnt into making movies anymore aswell as the additional cost factor.
Outside of a dog, a book is man's best friend. Inside of a dog, it's too dark to read. Groucho Marx

While Margaret Dumont is always a welcome addition to any Marx Brothers' movie, I'm not sure her 'wealthy dowager' character would have fit in the script anywhere. Remember, it was supposed to be a parody of
Casablanca
and there's just not a role that fits Dumont. I suppose they could have made her the owner of the hotel but that really would have been a stretch from the original script.