A sad situation, which obviously isn't working for you.
As to your 2 questions - your rights? - yes, to remain employed by the organisation in your current role until one party decides to change it or break the contract. And to be paid sick pay according to your T&Cs until it runs out and/or your employer decides you are no longer capable of delivering to your contract and decides to dismiss you (with notice).
At employment tribunal? - the only way of 'getting something' out of this is resignation then claiming constructive dismissal at ET. I am sure you will have explored this with your Union, who has all your circumstances at its disposal. Based on what you have told us, I don't think it would work. There isn't a sudden change to the job here that caused this. Please don't think I'm criticising when I say that 6 months out for stress when you've been out if the stressful situation for all of that time is likely to be problem for any employer. I have been faced with this situation before - it was a case of getting the person back to work a few days per week initially - then more days. The shear thought of GOING back to work was the core issue. But we are all different and I'm not diagnosing your problem. Maybe you just accept this job doesn't suit you - however it get another one through your employer (Government has a comprehensive cross-departmental vacancy advertising system - as i'm sure you know) you really need to be in work to try and take advantage of that. Could you face trying the CC job for a while in the sure knowledge that you were taking steps to get yourself out of the situation once and for-all?
In summary, I think it is trying to find a way of getting back to work to find another job, or facing that eventually your employer will tire and dismiss you on capability grounds. But I'll wager that your Union has suggested something similar to you.