No, grandparents is a common noun, therefore you don't capitalize it. It would be different if you had the names of the grandparents. Like if your grandma is named Martha. You would have to capitalize their name since it is a proper noun
The connotation of the common use of "dialect" is that it is used to describe or characterize a specific group of people. Thank you for posting your question. I hope this answer helped you. Let me know if you need more help.
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