This sentence and the English translation "your wife" does not make sense here. "Eure" is plural form of "your". This sentence could make sense only when talking to a bunch of men having one wife, as in a polyandry relationship. Not a situation you would come across in German parts of the world. On the other hand "Eure Frauen" could be right and make sense.
I've seen that too and it's not a typo. The nominative form is "euer". When you add an ending that 2nd 'e' gets dropped. I suspect it is because it is more awkward to pronounce 'euere', so that form doesn't get used much, especially in speech.
There are a few words that this happens to. "dunkel" means "dark". When you add endings, you drop the 'e' before the 'l', z.B. "dunkles".
I don't remember if there is a specific rule to help identify these situations. Maybe it's when there's an 'l' or 'r'.
Eure is the possive pronoun for you-plural -- second person plural. It's never singular.
Here is the best, clearest page I've found on this topic: http://german.speak7.com/german_pronouns.htm I pasted them into a document, cleaned up the formatting, and color-coded all the confusing hononyms. (I didn't bother with all the future and past tenses etc.
I do my best to remember or figure out where in the table the word I want is, enter it into the exercise first, and then look it up to confirm if I'm unsure -- I find if I look it up without thinking about it, I don't learn anything.