Thanks for everyone’s contributions especially to the user John’s insight into the toy soldiers without which I wouldn’t have had a chance of solving this!!
I believe the present wanted is:
(I had this as the original answer)
Snow at night!
Alternatively however because it’s too good to omit imo:
SNOW WHITE which makes sense considering there are 7 people in the family hinting at the 7 dwarves
Because
First paragraph:
Each present holds a clue as to the element which composes it completely or partially
Toy soldiers = Sn (tin)
Vial of water = Vial of H2O but what the vial of the formula, it’s the O since it resembles a container of a sort.
Scratch-resistant ring = W (tungsten)
In order consecutive order as hinted we get SN+O+W
Second paragraph:
Nothing = air or N for nitrogen (o for oxygen night)
Third paragraph:
Very strong and very light ring = Ti or titanium
Bracelet of deep red stone= HgS or cinnabar - s you get hg
Now the third paragraph hints at the reversal of letters in each stocking and the encompassing of the letters of the 6th stocking by the 5th so you get ‘ight’.
So we have:
snow night (a little pun on Snow White I presume)
Or alternatively:
Snow oight which sounds like linking this puzzle to Snow White!! and the seven dwarves which makes sense since there are 7 family members in the house).