Why did the Twins take Murtagh with them?

I searched the Eragon and Eldest sections and couldn't find anything about this.

Why did the Twins take Murtagh with them to Uru'baen? Was it more important to drag a 18 year old kid in front of the King than keeping their position among the Varden? They just have had Ajihad killed, if they stayed they could've used the chaos and make a great advantage out of it, for example secretely kill the next leader, or weakening the Varden with killing members of the Du Vrangr Gata. They also could've helped Galbatorix with inside information, for example about battle-tactics.

They may have scryed the King, and Galbatorix told them to bring Murtagh. If he did, Galbatorix must be an idiot.
Murtagh had no importance at the time, he was a nobody. Well, maybe he wanted revenge on him for escaping Uru'baen, but that motive couldn't be enough to make his only servants between the Varden leave their positions.
Maybe the Twins also told the King that Murtagh was Eragon's brother, and it made Galbatorix think that one of the eggs would hatch for him, after all his father and brother became Riders too? Well, he knew it since forever that Morzan was a Rider, so if he thought that family-ties have relevance in who becomes a Rider, why didn't he make Murtagh touch the eggs during the 15 years he spent in the King's castle? He wouldn't even had to force Murtagh to become his loyal servant!

But if it was really the first time Galbatorix thought about that Murtagh may become a Rider, why didn't he tell the Twins to give Murtagh to some Urgals that will lead him back to Uru'baen? Murtagh could've meant no harm to them as he was not able to use magic at the time. Or if he didn't trusted the Urgals, why didn't he tell that one of the Twins should fake his death and escort Murtagh to Uru'baen, while the other stays with the Varden and helps the King from inside? In my opinion, it's just stupid to give up such an advantage for a kid of no importance.

I know it would have been crucial for the story if the Twins satyed, but I still find this solution to make them dissapear a little amateur.

Does anyone have a sufficient explanation on why they decided to leave the Varden?