All perfect praise be to Allah, The Lord of The Worlds. May His blessings and peace be upon our Prophet Mohammad and upon all his family and companions.
The deceased person has sanctity and dignity since Allah, The Almighty, says {What means}: "We have honoured the sons of Adam"{Al-Isra`/70}. Sharia doesn`t permit exhuming or removing graves so long as they contain bones because the sanctity of their dwellers is similar to that of the living. In Jordan, it is well known that the bones of the dead need a very long time to turn into dust. About the sanctity of the dead, Prophet Mohammad (Peace and blessings be upon him) said: "Breaking a deceased body’s bones is exactly like breaking them when he is alive.” {Related by Abu Dawud}." He (Peace and blessings be upon him) also said: "It is much better for one of you to sit on a live coal, which will burn his clothes and get to his skin than to sit on a grave."{Related by Muslim}.
These narrations highlight the sanctity of the dead and show that preserving their graves against harm is an obligation. Therefore, not exhuming graves and not violating their sanctity is honoring their dwellers.
The place where the deceased is buried is considered a Waqf (Endowment), and it is better to bury the dead in a public cemetery because of the multiple number of the visitors invoking Allah for them. Since the above deceased is buried in a private cemetery, there is no need to move his remains to a place closer to his family to enable them to visit his grave and make supplication for him. In fact, this is no valid excuse to dig up his grave as it is possible to make supplication for him from any place, and his children are permitted to visit the grave as much as they can, if it is hard for them to do so.
In conclusion, it isn`t permissible to dig up the grave until after the deceased has disintegrated and no trace of him is left. And Allah the Almighty knows best.