As far as I know you cannot place a UI element on someone elses screen remotely.
If your addon is creating the raid wide dialog box, all people in the raid will need to have the addon installed to have the dialog box appear on their screen.
The raid leader would then activate the call to show the frame and the addon will wait for a response and relay the command to all people with the addon.
Those with the addon would then receive the command and the addon will respond to a receipt of that command by carrying out the appropriate request. And then send any response back to the addon as needed.
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