You should capitalize words like mom, dad, grandma, and grandpa when they're used in place of someone's name (thus making them proper nouns). Like: "Yo, Dad, toss me the car keys." (Sure, that language won't get you anywhere, but the capitalization is fantastic.)
Don't capitalize them when there's a possessive adjective in front of them: "My dad cries every time he hears a Joni Mitchell song. My mom hates it."
"Did you ask your grandpa to make one of his legendary rhubarb pies for Thanksgiving?"
"Can somebody wake up Grandpa? His snoring is driving me crazy."
Since grandpa is replacing the grandpa's name (you wouldn't say "Did you ask your George," would you?), it doesn't need to be capitalized. In the second sentence, though, Grandpa is used in place of what your grandfather's name actually is. To you, his name isn't Mortimer: it's Grandpa.