How to ensure sprites face the correct direction at all times in a 2D top down game. (logic)

I am making a multiplayer top down 2D game with 3d elements. All my movement, healthbars and basic functionality is working flawlessly even while hosted and playing on a server, node.js socket.io. However In this game it is possible to move the camera like in Realm of the mad god.

in case you are in doubt here is a video: https://youtu.be/4tdcxl3aZ0c?t=31s

This of course means that the players can end up being upside down with regards to each other and I cannot find a solution that works in all regards to make sure the sprites of the other players are always facing the correct direction with regards to their movement.

I have made several solution to this problem which cover most scenarios but while play testing other things we always end up noticing that the sprites sometimes face the wrong directions. So I am wondering if anyone has an answer, the logic, the fixing this problem.

Things I have tried:

Adding a gameobject to the camera to which all sprites asses their change in distance and determine their facing direction based off that information. (this leads to the players sometimes flipping erratically when the camera is moved and they as well are moving as sometimes they may be moving slower and there although moving left the camera approaches from the right and that flips them)
Adding a gameobject to the world which allows all sprites to have a fixed point to which they can measure their change in distance and therefore also know what direction to face (this worked somewhat better as they always know what direction they have to face, however once the player is upside down everything is inverted)
Emitting to the other players wether I am upside down or not in order to try to reinvert the above solution in the case I am upside down. (I could not find a good way to do this, and it got me thinking that this must be a problem people have fixed before many times and perhaps someone know of a good solution that works.)

thank you all for your input.

Solution

I seem to have found a solution for this issue that works decently well. Keeping in mind that I do not want to have the server being involved in this and I would rather have each individual sprite know its direction rather that have something heavy trying to determine this logic I came up with the following solution. May not be the best but it works. Still very keen to hear other solutions.

On my main character I have a switch case, which changes depending on the players rotation in the world. I need this switch case anyway for fixing (http://answers.unity3d.com/questions/1348301/trying-to-change-the-cameratransparencysortaxis-to.html?childToView=1348316#answer-1348316) that issue.

As the cases change I simply place the gameobject that I want the sprites to compare their distance to at 1 of 4 positions. YPos, YNeg, XPos, XNeg. Meaning that the sprite now determines its facing direction based on a gameobject that is placed in accordance with the Players position. without having to place it on the camera.

I will update if during further play tests this gives me trouble but thus far it works in the all the cases I need it to.

Still very willing to hear other solutions to this problem.

Thank you.