If Valentine is the Mortal Instruments version of Voldemort, Inquisitor Herondale is the Dolores Umbridge of the Institute. She acts like she's little Miss Rulebook but she's a crazy person looking for revenge in all the wrong places.
See, she hates Jace because her own son, Stephen, worked for Valentine and died. No, Valentine didn't kill her son. No Valentine didn't force him to work for him. No, Jace wasn't even born then and had nothing to do with it. So… this makes sense, how?
The Inquisitor has been driven insane by grief, and she's focusing all her anger on Jace. She wants Valentine to lose his son because she lost her own. She doesn't realize that Valentine doesn't give two hoots about his own son. He'd much rather play with his sword and his cup than have anything to do with his own flesh and blood.
When it comes to the Inquisitor and Valentine, we hate to admit it, but we side with Valentine when he finally tells her off. "Children make their own choices," (3.17.159) he says, getting her to see the error of her ways.
Because the Inquisitor seems to think death is the only answer to anything she sacrifices herself to save Jace. Ironically, her death keeps him alive. With her dying breath, she tells him something… but we as readers don't know what it is. Not yet, at any rate.