So I think it was a Manhwa.
The female MC reincarnated (died through suicide I think?) into a fantasy novel with a historical setting as a vampire hundred of years before the novels plot. She basically trains the male protagonists ancestor and supports his family to have the male protagonist eventually kill herself because she can't do it herself.
After the ML is actually born he has some psychological problems and becomes a shut in so MC uses her connections to become the Ml's teacher to solve it.

Other things I remember:

• she has a noble family that serves her and help her with becoming ML's teacher, they have red hair
• she rescues a crown prince that was supposed to die(?) and turns him into a vampire
• she secretly visits the ML right after he was born

Sounds like The Vampire's Plans to Die in Peace