PhD Dismissal after 6 years, how do I fight for it?

The timeline is still unclear.

It almost sounds like you left the PhD program (were you in good standing at that point?), got a teaching job, then realized you need to finish your PhD to get the visa you now need after 10 years, and are trying to go back.

At that point they reviewed your transcript/file and found that you were not eligible for funding and needed to do additional coursework. Since you have not met the requirements they set out for your return after an extended absence, they are dismissing you from the program.

If this is not accurate, laying out the timeline year by year may help people understand better.