What information are you trying to convey with the plot? Are you trying to present a summary or show the actual raw data in some meaningful way?
It will be great if I can represent the chromosome as a "line" but with the portions from grandpa (1) and grandma (-1) marked out.
Can you provide some more details about what you think this might look like? I immediately thought about chunking the genome into sliding windows and computing the proportion of each window being from grandma or grandpa and plotting that. Not sure if that is what you mean.