Snippets From TLH

Spoilers

In Nothing but Shadows, Brother Zachariah/Jem visited James in the middle of the night because James was in need, and because Zachariah was summoned to do so by the Dean of the Academy, who had no real idea how to deal with James's peculiar nature, and wanted the guidance of the Silent Brothers. Jem was certainly glad to be there, because he loved James, and was concerned for him. But it was not his idea to come. He was brought there in an official capacity:

And the presence of a Silent Brother in the Academy meant nothing good. Father was always inventing excuses for Uncle Jem to come to them-once he had claimed a flowerpot was possessed by a demon. But this was Idris, and a Silent Brother would be summoned to Shadowhunter children only in a time of need.

There seems to be an idea circulating that Jem should be spending more time with the people of his bloodline, specifically the Carstairs. That is an odd attitude to have about Jem, though, because the ethos that shared DNA matters more than love, dedication or actions isn't really congruent with his ethics or his stated beliefs. Yes, the Carstairs are his family, but so are the Herondales, and he doesn't have a history of privileging shared DNA over shared history.

For instance: Elias offered to take Jem in after he was orphaned, but as the two were never close, Jem chose not to go, because he'd already found a home (and a parabatai) at the London Institute. From Clockwork Princess:

"James spoke of you," said Elias. "After I left China, when I returned to Idris, I asked if he would come and live with me. But when I asked him if he would come to me in Idris, he said no, he could not. I asked him to reconsider. Told him I was his family, his blood. But he said he could not leave his parabatai, that there were some things more important than blood."

From Jem's perspective, the parabatai ceremony made him family with the Herondales. He would scoff at the idea that Alastair is more related to him than James in much the same way that an adopted child wouldn't have much time for the idea that their biological parent was their family in a way their adoptive parent wasn't. In Jem's view, the Herondales are his family (not his only family - and not to the detriment of the Carstairs, imho, but they are his family). Part of the message of all of the Shadowhunter books is that blood isn't love. The Fairchilds and Herondales and even the Lightwoods have done a lot for Jem in his life, where the Carstairs have done relatively little. Elias respected Jem's decision not to live with him, but as we know, afterwards, he wasn't particularly good at keeping in touch.

Of course, Jem would never blame Alastair and Cordelia for the indifference of their progenitors; however he does have a hard time actually getting to see them. Silent Brothers aren't allowed to come and go as they please. Their movements are circumscribed; they are expected to go wherever they are sent, and return to the Silent City when their mission is completed, with no dilly-dallying about. It was much easier for Jem to visit the London Institute than it would have been for him to chase down the Carstairs family as they traveled in Persia and France.

There's also the larger issue that after Jem became a Silent Brother, Elias actually worked actively to keep Brother Zachariah away from his family, which you'll learn more about in the Last Hours.

In spite of their father's wishes, Cordelia did develop a friendship with Jem, one that deepens over the course of the Last Hours. But Jem has had a more contentious relationship with Alastair. Alastair has always been creeped out by the Silent Brothers, and especially by the idea of being related to one. He tries to avoid Brother Zachariah whenever possible, to the extent of telling people that Jem isn't his relative, so you can imagine that Alastair would not exactly be pleased to be woken by him in the middle of the night for a surprise visit!

Could Alastair use some other influences in his life? Older, wiser souls to give him advice? Yes, he could. But Jem wouldn't be his top choice for the role. Alastair is just a kid in Nothing But Shadows, and he has a lot of growing up to do. Jem would be sympathetic to that, but Alastair is the one who has rejected him, not the other way around.