My learned colleagues have ably laid out the Halachic perspective in this matter.
The Reform movement has stated in past that it is not bound by Halachah, but Halachah and tradition are factors that are to be considered and followed where possible. Contrary to many assertions by those outside the Reform movement (and some within it as well), Reform Judaism does not stand for the position that 'anything goes.'
From a Reform perspective, it would seem to me that Jewish tradition and Halachah serve here as a guideline that is to be followed, but there is also a need for a balancing of interests and consequences. More specifically, based on the Mitzvah to honor your father and mother, it seems clear that a (reasonable) request by your parent is to be followed, as best as possible, and a final request (in contemplation of death) all the more so, due to the additional weight it carries.
For example, if a parent requests that a child not place them in a specific assisted living facility when there are several similar choices, that is certainly worthy of being considered and followed. Similarly, if a parent requests that a child not undertake 'heroic' measures to keep them alive at the end of life, that too seems worthy of consideration and should be followed.
At the same time, there would seem to be limitations on what a parent may appropriately request of their child, and those limits apply to final requests as well. For example, if a parent requests a child to murder them to end their suffering (along the lines of 'just bring a gun and shoot me!'), that is not appropriate and should not be followed.
The extremes at either end of this continuum seem clear; the difficulties arise most often in the middle, gray areas.
For example, in the medical arena, at the end of life if a parent has stated at some point clearly that they do not wish a feeding tube to be inserted if they are hospitalized, that is less clear than it might seem. If the feeding tube is being used for a two week period following stomach surgery, and the prognosis is that the parent will fully recover and return to an independent and active life, to withhold nutrition for that period (and risk killing the parent) by complying with the request makes little sense. On the other hand, if a parent has said that they do not wish to live in a long-term vegetative state, and they are comatose with no hope or expectation of recovery following a traumatic physical injury which has rendered them incapable of an independent or active life, to violate the expressed wishes of the parent and insert a feeding tube seems to be clearly inappropriate.
It is the middle ground where the questions arise. When the situation is murky, the outcome is not known, or the results are unclear, there is much more need to weigh the matter. If the parent who has suffered a massive injury in a car wreck has only a fifty-fifty chance of survival and recovery, and the degree of recovery is questionable, the question becomes much more difficult.
The difficulties come into play in the application of judgement and the assessment of the situation, and the balancing of the interests and consequences.
In this particular question, the issue raised specifically is in regard to final wishes, or last requests.
In this light, there can be no fixed answer, because the determination will depend on specific circumstances. When a parent makes a death-bed request that a child undertake some action on their behalf, the child will need to weigh the request. If a parent asks that the child give the parent's ring to a particular grandchild, or allow the grandchild to attend a particular school, that may be appropriate to follow. If a parent asks that a child disown a grandchild (that child's child), or convert and practice a particular religion or join a sect that the child has rejected, that would seem an inappropriate request.
If a parent asks a child to deal with their remains in a way that is abhorrent to the child or violates the child's moral, ethical, or religious beliefs, it would seem to me that it is not a reasonable request to make, and the child should not be obliged to comply; otherwise, as a way of honoring the parent, the child should do their best to do as requested.