If you have issues playing with mods during multiplayer with other people the problem is most likely to be your user script.

1) Open up windows explorer (the folder icon)

2) Navigate to %appdata%/The Creative Assembly/Shogun2/scripts

3) Open up user.script with notepad or another text editor

4) Arrange the mods so that they match the order of the other players mods

After that you will be able to play together with them using the mods.