Is this sentence correct; "Thank you for your letter about the missing items in both yours’ and your mother’s homes"?
The apostrophe in yours' is incorrect. See this question for a good explanation.
Otherwise the sentence is correct, but it's open to several interpretations. It might be clearer, albeit more long-winded, to rewrite it thus:
Thank you for your letter about the items missing from your home and from your mother's home.
As well as the apostrophe in yours' being incorrect in the OP's sentence, the word yours is itself incorrect. It should be your.