Obtainable chests?

Left of the iron mine in Dawn Star there is a chest badly hidden beneath the rocks. I believe it is the shopping chests of the khajiit Caravan. See this video for the instructions on how to obtain it. AFAIK there is no such thing as picking up the chest or adding it to your inventory. The game mechanics wouldn't allow that.

The Dawn Star chest was patched with the unofficial patch, but that is a mod, so you can disable it your self if you have it.

Most shopping chests are pretty well hidden deep behind walls/rocks/earth. It would be quite difficult to reach them on the PS4.
On the PC one could simply open the console and type tcl to toggle the collision off.

I believe you've misunderstood what you read, and that Mixiphoid's answer is correct.

If you are looking for more "portable storage", here is a list of options:

• When you level up, adding 10 points to your Stamina will also add 5 points to your carrying capacity.
• The pickpocketing perk Extra Pockets will add 100 to your carrying capacity.
• Fortify Carry Weight enchantments are available for ring, neck, arm, and feet slots. In addition, Thieves' Guild related body armor also carry the enchantment, as does the mask Volsung.
• The Aetherial Crown can hold the Steed Stone power for 100 carrying capacity, if Volsung's 20 isn't enough.
• Followers' own carrying capacity can be used as a convenient form of "Portable Storage".
• A Dremora Butler is worth another 148 carrying capacity worth of portable storage.
• Your carrying capacity is effectively unlimited when mounted. I find Arvak to be the most convenient mount in the game.

Though if you truly want game breaking carrying capacity, I've seen mods that allow you to have groups of followers at the same time.