City of Bones
We only get to see Clary's mother briefly at the beginning of the book before she's knocked unconscious and chained up in Valentine's asylum. And Valentine's her ex-husband, too! Talk about your dysfunctional marriage. She should have gotten a restraining order that prevented him from coming within 300 dimensions of her or her daughter. The poor woman is still in a coma at the end of the book, but here's what we know about her so far.
Through photos Clary finds and stories Hodge tells her at the Institute, we learn a bit about Jocelyn from when she was a young Shadowhunter girl named Jocelyn Fairchild. She met Valentine Morgenstern, who was everything a young girl looks for: strapping, charismatic, bent on world domination.
They had a child together, Jonathan Christopher, whom Jocelyn loved deeply. After the Circle's bloody plan was foiled, however, Valentine led Jocelyn to believe that young J.C. (no, not that J.C.. We're pretty sure this wasn't an immaculate conception.) had died in a fire. She fled Idris, pregnant with another child, convinced her first was dead.
Single Mom, Multiple Issues
Flash-forward fifteen-odd years to when Jocelyn is raising her daughter, Clary, in New York City. At first, Clary seems like a typical teenage girl with typical teenage problems, and so Jocelyn seems like a stock and standard overprotective mother. Luke has to tell her at one point that Clary's "not a pet, she's a teenager. Almost an adult" (2.86).
Her magic past is shrouded in secrecy from her daughter. Clary says that "[Mom] never talks about herself. [...] It's like her life started when she had me" (2.124). She even leads Clary to believe that the man she mourns for, Jonathan, is Clary's father, not her dead brother who didn't even live to see adolescence. That's some hardcore faking going on.
We'll have to wait until the next book to see if she and Clary and rebuild their relationship.