I did not originally make the mod, just wanted to be helpful providing instructions to set it up.
It may not work anymore or you may face the usual source engine jank.

To make the maps work in coop, you'll need custom files.
Download[drive.google.com]
Only the person playing Atlas (hosting/inviting) needs the files.

Once you've download the zip. you'll need to copy the files from the "maps" folder to your "portal2_dlc2/maps/" folder.
Windows path:
C:\Program Files (x86)\Steam\steamapps\common\Portal 2\portal2_dlc2\maps

Putting it in dlc2 makes it easier to restore the commentary back to default if you want to, by removing the files.

Get into a coop session, where you are Atlas.
Wait until the current map has loaded and you can walk around.

First, enter commentary 1 to enable the custom content.
Then, enter changelevel mapname, where mapname is the map you want to go to.

Good maps to start from:
sp_a1_intro2 - Skip the buggy container ride
sp_a2_intro - down the incinerator

Due to it being a singleplayer campaign, doors will close if one person passes them, so have sv_cheats 1 on to noclip through.

The game may sometimes crash or return to the menu.

Remember to set commentary 0 before starting a new multiplayer session or P-body will get an error message like #Valve_hidden_game. If it continues to not work, restart your game.

Some entity logic is broken and you may get stuck, in which case you may want to skip to the next level.

Wheatley turn-around, solution:
ent_fire @glados runscriptcode "sp_a1_intro7_TurnAroundNow()"

If you want the full immersive experience, do change_portalgun_linkage_id 0 to control the same set of portals as Chell (this may fix some issues).

This is a rewrite of this guide to be a bit more easier to follow. This mod isn't my own, but I enjoy it very much.