So the mothership needs to have a damage control module?
When you design a ship it will have a Damage Control number assigned to it.
Maintenance Facilities Engineering Sections (thanks Charlie) are multi-purpose equipment that lower breakdown chance, come with Maintenance Supplies, and provide a small amount of damage control, so just normal maintenance will allow repairing at a slow speed (and that may be sufficient for repairing light damage to small fighters).
The various types of Damage Control just increase the Damage Control ability of the ship, but they do so at a much higher rate than
Maintenance Facilities Engineering Sections.