First, let me say that it is not a ‘sin’ – it is simply something that we avoid in order not to disturb the peace and sanctity of the final resting place, or to negatively affect the honor or to cause any humiliation or embarrassment of the dead person or their memory (some of the same reasons we so often hear people say ‘rest in peace’). Judaism does not set these reasons aside lightly, however, each of these objections can be overcome, in given and specific circumstances.
It does occur that bodies are exhumed and reburied at times – for example, if the cemetery is being closed or otherwise is no longer acceptable, or has been affected by a natural disaster that compromises the location (the gravesite is next to a river and may be washed away, for example); if the body is being moved to be reburied in Israel or in a family plot; if a body is being moved to a grave acquired by the deceased, who intended to be buried there, but was not for some reason; or if the body was mistakenly buried in the wrong site (one belonging to someone else) and the owner (not a family member) wants to use it themselves and does not wish to sell or give it to the deceased or the family of the deceased.
In your question, there is a concern with the feelings of your mother, particularly in connection with her father-in-law, but those feelings are at some level opposed to the sense of honoring your father by leaving him to rest in peace in a perfectly acceptable grave.
Looking at the Halachic arguments, the Talmud in B. Sanhedrin 47b says:
“…An objection is raised: 'If one hews a grave for his [dead] father and then goes and buries him elsewhere, he himself may never he buried therein'?18 — The reference here is to a built grave.19 Come and hear! 'A fresh grave20 may be used. But if an abortion had been laid therein, it is forbidden for use'?21 — Here too, the reference is to a built grave.
Come and hear! 'Thus we see22 that there are three kinds of graves:23 A grave that has been found;24 a known grave;25 and one which injures the public.26 A grave that has been found may be cleared;27 when cleared, the place thereof is [levitically] clean and permitted for use.28 A known grave may not be cleared; if it has been, the spot is unclean and forbidden for use.29 A grave which injures the public may be cleared; if it has been, the place thereof is clean but may not be used'?30 — Here too, the reference is to a built grave. But may a grave that was found be evacuated? Perhaps a meth-mizwah was buried therein; and a meth-mezwah takes possession of his place of burial!31 A meth-mizwah is quite different, since its existence is generally known.32 “
Continuing, B. Sanhedrin 48a says:
“…Come and hear! 'A tomb12 built for a man still alive, may be used.13 If, however, one added a single row of stones for a dead person,14 no [other] use may be made thereof'?15 — This deals with a case where the corpse had actually been buried there. If so why [teach] particularly 'if one added [etc.]'; even if not, the law would have been the same! — This is only necessary [to teach that the prohibition remains] even if the body has [subsequently] been removed.16
Rafram R. Papa said In R. Hisda's name: If he recognizes that [additional row] he may remove it and the tomb becomes again permissible.
Come and hear! 'If one hews a grave for his [dead] father and then goes and buries him elsewhere, he [himself] may never be buried therein'?17 — Here it is on account of his father's honour.18 That too stands to reason. For the second clause teaches: R. Simeon b. Gamaliel said; Even if one hews stones19 [for a tomb] for his father, but goes and buries him elsewhere, he [himself] may never employ them for his own grave.20 Now, if you agree that it is out of respect for his father, it is correct. But if you say that it is because of designation, does any one maintain that yarn spun for weaving [a shroud is forbidden]?21
Come and hear! A fresh grave may be used. But if an abortion has been laid therein, it is forbidden for use,22 Thus, it is so only if it has actually been laid therein, but not otherwise!23 — The same law holds good even if it [the abortion] was not laid therein;24 and it [the statement, 'if it has been laid therein'] is [only] intended to exclude the view of R. Simeon b. Gamaliel, who maintains: Abortions take no possession of their graves.25 He therefore teaches us [otherwise].26 ….”
What we see it that the Talmudic argument would dictate that while you might be able to move your father’s remains, your mother (or any other relative of your father) would not be permitted to be placed in the grave from which he was moved - so moving your father to the grave next to where he was buried (and closer to his father), would not avail at all, according to Halachah and tradition.
Of course, all of this is following the approach of tradition and Jewish law: from a Reform perspective, there are a number of Responsa that apply.
First, http://ccarnet.org/responsa/carr-172-173/, which determined that disinterment and reburial to move a body to a family plot was allowed, determined by the appellate division of the supreme court of New York, 1900.
Secondly, in 1922, a similar issue arose and was answered in the affirmative in Responsum http://ccarnet.org/responsa/arr-353-355/.
It would seem that disinterment (exhumation) and reburial are permissible within the Reform context, at least in some instances. However, I do not find any materials that approve of it for the reason that the surviving spouse does not wish to be buried next to another relative.
The solution you propose seems simple, but I can’t find support for it in text or in prior decisions, and frankly, it just ‘feels’ wrong. Consequently, I would suggest that your mother be counseled and helped to reconcile herself to the way things now are, rather than follow the course that you ask about.
If she is adamant and insists, then you will have to determine whether the cemetery operating organization would be willing to consider the request. If not, and your mother persists in her request, you would need to think about acquiring graves at another place, and pursuing reburial of your father elsewhere, and burial of your mother at that location. This makes me very uncomfortable, as it has the effect of removing your father from his family plot – precisely the opposite of one of the considerations that permits exceptions to disinter and rebury in Jewish practice.
I sincerely hope that you can persuade your mother to reconsider her request: that would be the easiest and best outcome.
Rabbi Joe Blair