By race-logic, didn't the parents of disabled children come under suspicion? I suppose that the difficulties coming to families with children with disabilities were too common for Nazi doctrine to take too scorched earth views; too many Nazi supporters had disabled children in the family.
But while the Reich was often out and proud about just how cruel and ruthless they were demanding people to be, they did sometimes sneak and slink about rather that forthrightly act. The laws demanding that people with serious disabilities be executed (I think "euthanized" is an ugly word itself, but not quite ugly enough for this) came rather late and serious enforcement later, and they liked to do it quietly and deceptively. There were two prongs of unexpected resistance that caused the regime to back off and let be, or anyway wait until quiet opportune moments when no one seemed to be watching--one was the Roman Catholic Church, which had a lot of the disabled in its care; the bishops took very stern positions on this. Another was the fact that people might well worry that a soldier (or conceivably industrial worker, or agricultural worker on any level, in a fit of hard work to meet increasingly demanding wartime goals, overworking and neglecting safety) might suddenly become disabled, and the fear was the regime might do away with war wounded along with the congenitally disabled.
Still, one expects that with victory, they would get around to stuff they put off dealing with earlier. Sooner or later the authorities were going to do away with disabled people, and any social factors that might delay that day of reckoning would raise the issue of forced sterilization instead. Now of course genetic science was poorly understood in the 1940s and Nazi ideology was another factor muddying the waters; some disorders might have been treatable and/or unrelated to genetics at all. But aside from the mysticism of purifying the blood, there was the Nazi notion of pragmatic cost-effectiveness too; even understanding that wartime wounds of severe nature are in no way a reflection on the genetics of the solider who happens to catch a round or seven the wrong way (though some smarmy characters might suggest the soldiers with the best genes were the ones who avoided getting shot up--it should be clear enough why some Heer officers overhearing that line of reasoning would put the Army's authority behind tabling the program of "hygine," if one imagines how the morale of front line fighting men might be affected--after all, the cowardly soldier who lets others take the biggest risks seems to be held up as the example to follow here!) still, now that they have no face or are missing limbs or whatever, it costs as much or more to maintain them but they can't do as much productive work, so shouldn't the Volk, um, prune them off the branch, good genes or not? Anyway plenty of disorders would be deemed up in the air scientifically, and a racial hyginist might well say better safe than sorry, and to be blunt, there are plenty of mediocre, merely acceptable, blood lines around; no harm (from the racial point of view anyway) in treating dubious outcomes as a sign of hidden flaws, better safe than sorry.
So--although it may be that never in the years of the Nazi regime OTL, was it ever proposed to sterilize or worse the relatives of a person with congenital defects of an apparently genetic origin, I suppose that within a couple years of declaration of victory, if that long, the ruling would come down that parents of children with disabilities should be stopped from reproducing, if not simply executed along with their child. "Better safe than sorry!"
It is a peculiarity of this TL though that the author has decided, reasonably in my view, that for this that and other reasons, the much-touted engineering and general economic enterprise of the great Germanic-Aryan people (as they thought of it) would run out; that between the sheer mass extermination their established policies called for, general wartime devastation, and the general economic clogging of the arteries due to the well off (those who passed in the racial purges anyway) lacking serious competition and falling into complacency while lowly labor was increasingly deemed fit only for slaves, the Reich would become a stagnant mess. In particular the great explosion in births that the regime counted on (and I think did get to some extent in the 1930s) would misfire.
Facing stagnant populations it seems the SS and other racial "gardening" agencies seem to have become rather expedient in their definitions of satisfactory Aryanism, and this might well mean that after all, the regime really can't afford to sterilize every couple who produces a child with any sort of disorder whatsoever. I am sure the children themselves are ruthlessly slaughtered anyway, but maybe the parents just get noted down as people to watch for more possible trouble, either in their emotional reactions to being branded parents of unfit offspring, or in having more children with visible or worse, hidden, defects.
But it could also be that one reason for the stagnant population growth rate of the Reich is that its minions are still zealously at work on this "Great Work" of genetic purification.
Whatever, I quite understand Eike's desire to ignore the call, let some other slobs with the right mix of zeal and calloused attitudes handle it. And the distraught state of the mother could have nothing to do with the threat of death or mutilation for herself, her grief for her child putting all those things aside for now.
Indeed this must be so, for if an obedient daughter of the Reich stoically hands her less than perfect offspring over to be discarded, and need fear no blame for it, woe to anyone, no matter what their sex or blood pedigree, who disobeys. She could be the perfect paragon of Aryan womanhood, but her very disobedience is evidence deemed to show a fatal flaw in itself.