My mother is a longtime Catholic. She dragged her six kids to church every Sunday for years and years. She left us in the pews and went to the back of the church to cry because those four boys of hers wouldn't sit still and be quiet. Poor woman. Anyway, she had this locket with a little bit of what looked like a bone fragment in thee, which she called a relic, and it was supposed to be a little piece of some saint's body. I don't know if it was real, but she thought it was. I wasn't the only one in existence, so I assume that it may be a common practice amongst Catholics to hold on to some physical piece of a historic church figure. Talk about being parted out!
Your mother had what’s called a “First-Class Relic” (i.e. an actual piece of a Saint’s body), which is rather uncommon for a Catholic to have, BTW. For reference: second-class relics are pieces of items owned by the Saint, and third-class relics are items which have been touched to a first-class relic (or the tomb, or a second-class relic, if the [1st class] relics of the Saint are not available).
As for relics: look at 2 Kings 13:20-21 for an example of how Biblical the idea is, and how God can work through them. You can also find a reference for the basis of 2nd-class relics (cf. Matthew 9:20-22) and 3rd-class relics (Acts 19:11-12).
As for “not being able to leave dead people alone”, two comments:
1) John Paul is not dead. “[God] is not God of the dead, but of the living.” (cf. Mark 12:27)
2) How is the veneration of JP2’s relics in any way disturbing him, or disrespecting him?