One thing this looks to miss is that what you are socially constructing is a constraint. And so any distinction remains irreducibly vague in practice. It does carve the world up into differences that make a difference. It does impose informational boundaries around the world and its physical dynamics. But a constraint only narrows the scope of a meaning or intent to the degree it is considered (socially or organismically) useful.
So talking about stuff is vague. It has vast scope in language when it comes to bounding the world with a meaningful distinction. But a combination of words, said in this particular context, then should narrow the scope of an intent with great precision.
Your kids should understand that the intent they are meant to mirror - the constraint they should place on their own physical or dissipative degrees of freedom - don't involve tidying up dead spiders or doing something about the chairs.
The very fact you can imagine labelled boxes - physical constraints of the most literal kind! - for all this loosely referenced "stuff", shows how socially constructed this real world landscape really is.
By the by, all this is precisely what Peircean semiotics and modelling relations approaches make clear.
Spencer-Brown is only half getting it in talking about the triadic nature of the informational side of a model's epistemic cut. He talks about the symmetry breaking that creates the three things of the two domains distinguished and then the third thing which is the boundary or act of division imposed.
The full semiotic view emphasises that the modelling relation is between an informational model and an energetic physical world. There is an ontological duality, a self/world, that is being constructed. But this is triadic in that the self forms signs of the world. It is the whole point of modelling not to represent reality in some veridical way - leaving no gap or epistemic cut between self and world - but to instead form a habitual relation of signs that comes to be our understanding of the thing in itself.
So biologically, the physical energies of the world are experienced by us in a perceptually constructed fashion. We see red and not green as a striking difference when the physical wavelengths may be only fractionally different in reality (and in reality, not at all coloured in any sense).
This is of course where SX goes particularly astray. If you conflate self and world, ignore the epistemic cut, then you start to talk about hues as "the real" and you don't assign them the proper ontic status of being our mediating signs of physical energies - a translation of the material world into the information that habitually constructs a state of mental constraint on our intentionality. Seeing red or green can mean something ... because they are in fact never real. We can then impose whatever intepretation or habit of meaning we like as they are just symbols.
Anyway, this semiotic game is then repeated at the social or linguistically mediated level of experience. We carve the physical world with useful concepts like boxes, kinds of toy, tidiness, parent-child dominance relations, etc.
So going to the OP, semiotics would take it as obvious that our relations with the world are constructed. That is the definition of life and mind - to be a modelling relation where information forms a self in fruitful control of a physical world.
And the typical reaction to this realisation - that conscious awareness is indirect or constructed - is negative. It seems an epistemic problem rather than the necessary basis of an epistemic relation. Most folk are naive realists and want philosophy to get them back to that happy position somehow. But the whole point of awareness is to simplify the complexity of any physical environment and to take advantage of its entropic gradients - tap the flows for useful purposes. So the world has to be replaced by a system of signs. Constructing "our world", our umwelt, is the same as constructing our selves, our own individuated being and meaning.
Humans depend on social construction to be human. It is not a bug but the feature.
The only issue then is whether there is a natural story of progression. Is this a pluralistic free for all where anyone can make up their own valid worldview, or is there a real world out there and so the world construction must converge on some optimal mental model?
Again the answer seems obvious. The scientific view of reality has arisen as a modelling discipline which is most effective at constructing the constraints which can harness material flows. Science is the most life giving way of construing the world.
Of course then you can look around and protest at the state of a scientific society. But any biologist will tell you how out of kilter with nature we have allowed things to get. Modern society is not being rational on the long term view.
But again, the bottom lines are that any relation with the world is a process of triadic mediation. We have to form the signs that become our world and so form our strongly individuated selves along with that. That is the essential epistemic relation.
And then there can be many ways of setting up that self-world point of view. The social constructionist arguement becomes about which socially encouraged stance is evolutionarily optimal. And that question can't be answered without recognising that the relation is between the information that constructs constraints and a world of physical potential that is being thus usefully constrained.
So any epistemology has to be grounded in a natural ontology. And people know that. It is why social construction is treated as such a danger - this idea that folk can construct their own realities rather too freely.
But in fact, against naive realism, it also had to be understood that what constitutes our psychic reality is the third thing of the modelling relation. We shouldn't mourn the impossibility of knowing the thing in itself. The whole point philosophically should be attending instead to forming the healthiest system of signs - the correct mediated view. What would it be to optimise the modelling relation (in some given environmental context)?