Maybe this is the only way to convince my fiancee to play with me...
Also, if it works, will be a good reason to buy the expansion
That's a good reason to play co-op!
It's possible, sometimes I 'turn off' a lot of the Expansion and Advanced rules when I teach the game using the co-op scenarios. For Doomsday I would:
-Pretend your 20 CP Homeworlds are 30 CP Homeworlds.
-Start with Terraforming
-Use the "Black Hole Jump" technology as described in the Expansion Scenario Book
-Since you can't really use Titans, I would make all Doomsday Machines have the weakness to large fleets, that way you and your teammate can build Dreadnaughts and smaller ships to beat them.
-Since you can't capture planets with ground troops I would make destroyed planets count for fewer Victory Points for the DMs.
The Alien Player scenario doesn't work as well as a teaching game since theres a bit more moving parts.