So I thought, too. I completed her quest. Much later, she mentioned that she's only interested in the dark side of alchemy, so she's carrying on the family tradition in her own way.
Sez you.
How do you know she doesn't plan on poisoning Mommy Dearest herself... if only the PC could accomplish such a feat.
EDIT: If you complete her quest, every few game days, you can loot her chest down in the alchemy shop for whatever it's worth... at level 36+, it's worth a LOT. Blacksmith's Elixirs, Enchanter's... Etc...
If you're not an Alchemist yourself, it's a never-ending treasure trove.
And, no, she never back-stabs you.