The boys' grandmother, Diane Mathena, wants Tyler and William Jensen buried next to their father in Palisade, while the mother wants them cremated.
According to the Grand Junction Daily Sentinel, the remains have already been turned over to a funeral home for cremation, but that's now on hold.
The mother, Heather Jensen, has not responded to requests for comment.
So far, no charges have been filed after 4-year-old Tyler and 2-year-old William were found unconscious after their mother left them alone in her SUV more than a week ago and they later died.
(Copyright 2012 by The Associated Press. All Rights Reserved.)