Alright then, that's the problem, you are still referencing everything from the other mod!
Solution is simple, find the code for the thing you want to edit, and change the paths for the sprites to the sprites you want to use now.
For example, if you copied Coalition.rte and your new faction is called CoalitionResprite.rte (or w/e, really), and you want to edit the sprite of the assault rifle, you'd go to CoalitionResprite.rte/Devices/Weapons/Machineguns.ini, and look for a line that reads
Code:
SpriteFile = ContentFile
FilePath = Coalition.rte/Devices/Sprites/RifleSubAutoA.bmp
There you'll change the FilePath to the path of your new, edited sprite. Now, the line below of that should say "FrameCount = X", where X is the number of sprites used for the weapon. If you use only 1 sprite, set it to one, otherwise it'll give you an error.
I hope I was clear, else, ask again