Ina ultimately chose to join the Sisters of Silence. It was her own decision.
Ina had not been happy in the Chapter.
She wanted to fight shoulder to shoulder with the warriors, facing the oncoming forces of Chaos back to back, rather than merely standing at the door to welcome them home.
You were born to fight. I can give everything to fight alongside you.
Repairs to the warship proceeded quickly. With the Techmarines leading the work, the Adeptus Mechanicus personnel threw themselves into repairing the Black Ship.
The local stockpiles of metal took a considerable hit. The materials needed to repair the Black Ship were precious, too.
During the repairs, the various Astra Militarum forces were only permitted to interact with the Atris Astra Militarum. For one thing, they needed to undergo screening for Chaos corruption, and without an Inquisitor present, the Astartes could only lead the Atris Astra Militarum in conducting it.
For another, it kept them from going down to the planet and arguing with the people over whether the Emperor was a god.
The Sisters of Silence were another matter. The moment they spotted a Lunar-class Cruiser parked in orbit, they wanted to make off with it.
Evan stopped them on the grounds that it was the Atris Astra Militarum's only warship.
If the two Lunar-class Cruisers had not been severely damaged in the previous battle and towed away for repairs by the Adeptus Mechanicus, who knew how many might have been taken?
Get them out of here, quickly.
As the price of sending them on their way, the Crimson Tide Chapter would dispatch twenty warriors to join their expedition. They could treat it as joining the Deathwatch to help out for a few decades.
In any case, on paper, the Chapter only had the two