Greetings.

Since the Vaulters update (or mabye a week early, I am not certain anymore) whenever me and my wife play any multiplayer match, the start of any turn take quite a while (about a minute, and it is slightly shorter for whoever the host is) before letting us perfom most actions: cannot set buildings, move fleets, engage in diplomacy, level up heroes etc...

This isue however does not appear when any of us plays the game single player.  The games we host are protected and we are connected over the internets's provider modem, with open NAT. We also both reinstalled the game, updated windows, updated graphic drivers (we both use NVidia cards) and did a small prayer to the Virtual Saints.

Thank you in advance for any help or tips. 

First, battles in endless space in multiplayer freeze commands that can be given for other players, so if your friend/wife is in a battle, you will be locked out of action until the battle is resolved. Also in ES2 lag is usually pretty bad because most games are played accross clients in different continents.  A solution is to have the host of the game be the PC with the strongest internet and located geographically closest to all the players in the game.  Thirdly, a battle timer that requires a battle to be completed in 30 seconds also helps, because it forces a resolve 30 seconds into the turn allowing you to do actions normally.

As you get accustom to it you can que buildings and such without having them show up (knowing eventually they will once your commands ping off the host and come back to your PC).

Generally speaking, ES2 is not very LAG friendly, it never has been, its better than it wasm but unfortunatly that doesn't change the fact

If its possible your internet provider is throttling your internet that may be a isssue, as that goes un-announced to the customer, but it sounds like you've done your homework and done the best you can to make your gaming experience pleasurable.  I hope this helps, I know its not much, but its something.