The extent of Domnall's rule in the kingdom is unknown, and it is questionable whether he had any real authority in the northern Hebrides, the islands furthest from Mann.
In about 1097, Magnús sent Ingimundr to the Isles to take possession of the kingdom.
After installing himself in Lewis, the chronicle reveals that Ingimundr was overthrown and killed whilst in the midst of securing the kingship.

And when he had arrived in the island of Lewis, he sent messengers to all the chieftains of the islands; ordering them to assemble together, and appoint him their king.
But meanwhile he with his associates abandoned himself to robbery and banquetting; violated the chastity of women and girls; and devoted his attention to the other pleasures and allurements of the flesh.
And when this had been reported to the chieftains of the islands, when they had already assembled together to appoint him king, they were fired with excessive rage, and hastened towards him; and coming upon him by night, they burned down the house in which he was; and annihilated him and all his men, some with the sword, and some in the flames.

— Chronicle of Mann, an excerpt concerning Ingimundr's arrival and ruination in the Isles.

Ingimundr's rationale for seating himself upon an island (Lewis and Harris) on the edge of the kingdom may have been due to his inability to gain any authority on Mann itself.
The chronicle reveals that civil war erupted there the following year, and the twelfth-century Historia ecclesiastica indicates that Mann was devastated to point of being a virtual desert by the time Magnús appeared on the scene.
The warring itself may have been related to the factional struggles between Guðrøðr's sons.
Although it is possible that it was Magnús who actually forced Domnall from the Isles, the fact the chronicle makes no mention of Domnall during the recorded conflict on Mann may be evidence that he had lost control of the island by then.
Within the year, the same source records the arrival of Magnús, which could suggest that it was Ingimundr's slaying, at the hands of the Islesmen, that had incited Magnús to take matters into his own hands.

There is little known of the inauguration of kings in the Isles.
What is apparent, however, is that the so-called chieftains of the Isles—or principes Insularum—played a significant role in king-making.
Although Guðrøðr had originally gained the kingship through conquest, the chronicle reveals that his later descendants relied upon legitimisation from the chieftains.
For example, this source notes that it was the "noblemen of the Isles" who had approached Muirchertach to intervene in the Isles following the strife between Guðrøðr's sons, and it was "all the chieftains of the Isles" who drove (Muirchertach's delegate) Domnall from the Isles not long afterwards.
Furthermore, following Magnús' eventual death in 1103, the chronicle records that it was the "chieftains of the Isles" who sent for (Guðrøðr's son) Óláfr to occupy the throne.
The extent of Domnall's rule in the kingdom is unknown, and it is questionable whether he had any real authority in the northern Hebrides, the islands furthest from Mann. In about 1097, Magnús sent Ingimundr to the Isles to take possession of the kingdom. After installing himself in Lewis, the chronicle reveals that Ingimundr was overthrown and killed whilst in the midst of securing the kingship.
And when he had arrived in the island of Lewis, he sent messengers to all the chieftains of the islands; ordering them to assemble together, and appoint him their king. But meanwhile he with his associates abandoned himself to robbery and banquetting; violated the chastity of women and girls; and devoted his attention to the other pleasures and allurements of the flesh. And when this had been reported to the chieftains of the islands, when they had already assembled together to appoint him king, they were fired with excessive rage, and hastened towards him; and coming upon him by night, they burned down the house in which he was; and annihilated him and all his men, some with the sword, and some in the flames. 
— Chronicle of Mann, an excerpt concerning Ingimundr's arrival and ruination in the Isles.
Ingimundr's rationale for seating himself upon an island (Lewis and Harris) on the edge of the kingdom may have been due to his inability to gain any authority on Mann itself. The chronicle reveals that civil war erupted there the following year, and the twelfth-century Historia ecclesiastica indicates that Mann was devastated to point of being a virtual desert by the time Magnús appeared on the scene. The warring itself may have been related to the factional struggles between Guðrøðr's sons. Although it is possible that it was Magnús who actually forced Domnall from the Isles, the fact the chronicle makes no mention of Domnall during the recorded conflict on Mann may be evidence that he had lost control of the island by then. Within the year, the same source records the arrival of Magnús, which could suggest that it was Ingimundr's slaying, at the hands of the Islesmen, that had incited Magnús to take matters into his own hands.
There is little known of the inauguration of kings in the Isles. What is apparent, however, is that the so-called chieftains of the Isles—or principes Insularum—played a significant role in king-making. Although Guðrøðr had originally gained the kingship through conquest, the chronicle reveals that his later descendants relied upon legitimisation from the chieftains. For example, this source notes that it was the "noblemen of the Isles" who had approached Muirchertach to intervene in the Isles following the strife between Guðrøðr's sons, and it was "all the chieftains of the Isles" who drove (Muirchertach's delegate) Domnall from the Isles not long afterwards. Furthermore, following Magnús' eventual death in 1103, the chronicle records that it was the "chieftains of the Isles" who sent for (Guðrøðr's son) Óláfr to occupy the throne.
Assassination of Ingimundr