Your home or a park isn’t holy ground, like a Catholic cemetery or a Catholic church. Holy ground blesses the dead bodies kept within it (or upon it, in the case of Catholic mausoleums and columbariums) and allows the souls of the dead to share in many prayers (particularly the cemetery visit indulgences granted on All Souls’ Day and the month of November). It’s also a sign that our dead bodies (even in ash form) are not just trash to throw aside, but loved and protected by the Church. Our bodies are also part of the Body of Christ, and wait in hope for the Resurrection. A lot of people aren’t aware of all this, these days, and that might include your parents.
Official teaching material about funerals, burials/ash inhumation, and holy ground might help. Sometimes parents won’t just take your word for something; they like to see it in black and white from several sources. They might also take a while to change their mind and accept the “new” teaching they’ve learned. People don’t like learning they’ve been kept ignorant of something important, or that something they were told had changed after Vatican II really hadn’t.
It was a sad thing to have to be buried at sea, or to have your body left unburied or unfound. There was no stigma to those unfortunate dead; but it was something people prayed not to have happen to them. A happy death with the Last Rites, and a Christian burial until the Resurrection, were what people desired.
Being purposefully buried outside of holy ground used to be regarded as a terrible punishment, reserved only for the worst unrepentant sinners, or for people who had sadly never become Catholic or Christian. Suicides used to be buried in such a way, but later the Church came to believe that it was too terrible a fate for people who might after all not have meant to kill themselves out of hatred and defiance for God and all life.
In popular culture and in benighted places in Eastern Europe, scattering ashes to the four winds was what you did to make sure a suspected vampire or evil undead wizard would stay dead and be unable to put himself back together. It was the ultimate expression of hatred and disgust for a person. You might want to find your parents a copy of the Russian fairy tale “The Death of Koschei the Deathless”, aka “Marya Morevna”, for an example of this! It’s in Andrew Lang’s The Red Fairy Book, among other places.
This sort of thing often really distressed Catholics whose children were killed in war and had their bodies lost or blown up, which was part of why priests stopped emphasizing the burial rules after WWII. But it’s gone too far the other way, these days, so that people forget how integral that proper funeral customs are to life, from the earliest days of Judaism and Christianity.
Good luck on trying to teach your parents and family. As you keep trying, talk to God about it, and maybe He’ll arrange for a lot of mysterious recurring homilies and television shows about what they should be doing.
