Yes.
The ability to summon the chest is part of the effect of the spell and not of the casting.
While the chest remains on the Ethereal Plane, you can use an action
and touch the replica to recall the chest.
Since you do not have to cast the spell, whether it is prepared is irrelevant.
When items go to the Border Ethereal, they don't have to move.
DMG 48 says that every location on the material plane overlaps with the corresponding location on the border ethereal plane:
The Ethereal Plane is a misty, fog-bound dimension. Its "shores," called the Border Ethereal, overlap the Material Plane and the Inner Planes, so that every location on those planes has a corresponding location on the Ethereal Plane.
Therefore, if you're simply moving the chest from the material plane to its corresponding location in the Border Ethereal, there is no movement per se.
This interpretation is consistent with the Ghost's etherealness ability, which allows it to move freely between the two planes (MM 147):
The ghost enters the Ethereal Plane from the Material Plane, or vice versa. It is visible on the Material Plane while it is in the Border Ethereal, and vice versa, yet it can't affect or be affected by anything on the other plane.
Note that while doing so costs the ghost an action, it doesn't cost it any movement. Additionally, while it's technically on another plane of existence, the Glyph of Warding spell doesn't address different planes, so I suppose it doesn't apply.
Leomund's Secret Chest is unclear
It's clear that if you summon your chest to yourself while more than 10 feet away from its original location, your Glyph of Warding spell will end. However, the text of the spell is a bit ambiguous as to where exactly on the Ethereal Plane the chest goes when the spell is initially cast.
If it just enters the Border Ethereal at its current location, then your plan will work, but if it goes somewhere else, then it won't. Given that the text doesn't specify, this will have to be something you work out with your DM.
Best Answer
The death of the caster does not cause the spell to end. To start with, the spell is instantaneous. You cast it, a chest is hidden, and the spell is done. However, the spell lists all the ways it which its effect can end:
So the caster dying will not end the effect of the spell. However, only the caster can use the replica to recall the chest from the Ethereal Plane. The spell (like most spells) consistently uses "you" to refer to the person who cast it. In fact, the entire chapter on spellcasting uses "you" to refer to the caster.
That being the case, while the effect of the spell does not end with the caster's death, the larger chest is, for all intents and purposes, lost forever as soon as the caster dies. There might be one way around this, though. The chest is only "irretrievably lost" once the effect of the spell ends. Until that point, it is hidden on the Ethereal Plane. While the nature of that hiding is unspecified, it certainly seems possible that you could travel to the Ethereal Plane and look for the chest there.