You can get two separate supply icons. You just have to custom make the one for protoss. Basically just make a small dialog with background image set to black.dds and add an image dialog item for the supply icon and a label item for the readout, and periodically update the label to read out the protoss supply usage.
I dunno then. You could have a trigger detect whenever that player created a protoss unit and then Set Unit State: Uses Supply off, and then manually handle the supply used with your own integer variable... but you still wouldn't be able to make a protoss unit if you didn't have sufficient spare supply. I guess you could go through each protoss unit in the editor and remove the supply requirement... but that might not be appropriate to your map.
EDIT: I just made a test map where i had no issue building marines via player 2's (ally with shared spending) barracks.
I just set up the alliances and made sure player 2 had enough minerals and supply. I do not seem to have run into whatever issue you are having.