The OP mentioned using the ASCOM ScopeDome application. This is a hub that connects to both the scope and the dome and manages the dome slaving independently of SGP.
In normal use it monitors the scope position and adjusts the dome azimuth so the mount can see out but if it sees a slew command being sent to the scope it will use this position to calculate the dome azimuth and slew there while the scope is slewing.
The scope Slewing property should wait for both the dome and the scope to report they are not moving before returning false.
You should not need to inform SGP about the dome at all, but...
I've never tried it but it may be possible to set up SGP and say that you have a roll off roof. Specify ScopeDome for both the telescope and the dome and set up the 'dome' as a roll off roof in SGP. This should mean that scopeDome handles syncing so the scope can see out and SGP opens and closes the shutter as it feels fit.
It's not possible to comment without considerably more detail about what 'not works' means. We need details of exactly what is happening, with numbers. probably also log files.