Greetings,
Deputation and relocation are a part of job rotation. It may not essentially remain pleasant or aligned to personal targets. However, you have agreed to 'Employment at will' in your appointment letter. Hence, you need to now chart your way to the point where you want to be.
Discussion with your leaders and reporting managers, is the first way out. Please manage this very carefully. A request for a change is a direct disobedience to the orders given to you. Stay away from it. No matter how much it feels bad, try and figure out how best can you deliver in this new role. Initially, you will find many more reasons to fail than to succeed.
Irrespective of your feelings and your prospects, please try and put your best efforts to this role. If you are supposed to request for a transfer to your old department, it would only be possible if you have tried your best in the existing role.
Scan for every reason how you could add value to the role if transferred. However, keep your expectations low. Any transfer is made after a complete brain storming. No management would take a request to re-consider it easily. So work your way through. Connect with your mentors in the organization and chart on how to proceed with the request.
Be prepared for every adjustments in terms of comfort zone. Research well on how you could add value in the option requested for. Remain vigilant, as every opportunity discussed with you during this negotiation, might be far better than the former role.
Wish you all the best.