Historians should investigate LKY and KGC personalities and mindset.
Were they a bit psycho/ sociopathic?
When KGC said, in LHL's words,  "his mother's distress at the thought of strangers traipsing through her private spaces long after her death". 
https://www.straitstimes.com/opinion/straddling-fine-line-between-public-and-private-wishes
Why did she say that. Was she out of touch with the ground? Was she an unwilling spouse to a strongman in power, does she distrust the country her husband ruled over?
What is the basis of her paranoia? Does she have insight into the hatred she or her husband have attracted, and thus on the defensive? Was she demented after her stroke and speaking under the duress of dementia? 
Did LKY follow her whimsical wishes, but stricken with fear that historians will judge him negatively with the consequence that his family 'mausoleum' would be desecrated by his enemies or a public display of his stature, too soon forgotten by most?
This kind of instructions about a post life existence, either entombed in a mausoleum or other sophisticated monument creation in positive or negative sense,  seem born of the period of monarchs with royal rule under sacred auspices in the Roman or Egyptian empires, it's unusual in a modern democracy, especially where laws prescribe presidential term limits (USA and in fact also communist China)  or even in Singapore, a purported parliamentary democracy where probably over 95% or more of citizens have little say on their abode (being strata titled or lease holds) and thus cannot fathom such post life demands and rightly, the siblings cannot agree on LKY's wishes because they are totally out of touch with the age we are in now. A more realistic and humble home owner would have demolished whatever property he felt had sacred status (and thereby impermissible for lay citizens to enter) and made orders to ensure such, whilst one was alive to ensure so. To demand  compliance after death, especially when there were already contentions, as yet not make it explicitly clear having been recorded on video demanding destruction, perhaps shows that LKY was possibly already showing some symptoms of dementia or was suffering some delusions of grandeur, when he made such peculiar orders, imagining he actually held the authority post death, when indeed, the political machinery he created gave him no right to do so.
Self pwn.
LKY is just a man, who also has to get a taste of his own medicine. God is fair and karma does bite all.