Are you using 1 single action in your script and assigning it to both entities?

It is best to create 2 seperate actions for each entity you want to control..

ENTITY* player_1
ENTITY* player_2

Action 1
{
player_1=me;
.....
walking code
}

Action 2
{
player_2=me;
.....
walking code
}

So now you can control each entity individually, depending upon the controls that you assign to them.

Don't forget to assign the right action to the right entity in WED.