If you're not familiar editing .ma files make a backup first, it's veeery easy to do something wrong and corrupt your file forever.
Also, two suggestions:
First, when referencing a model, do it without materials, and apply them on the referenced model later. Maya very often has issues with this. If you need to reference the model several times, you can create a script to apply the materials/textures to all your objects. This you can do by copy/pasting from the script editor if you are not familiar with mel.
Second, Try to avoid parenting geometry to other geometry. Preferably use grouping and parent constraints and keep geometry separated. This could very well be your problem, since when applying a material Maya applies it to all the geometry parented below.
Where you able to fix the issue?