Neither expression works well.
Insatiable refers to a desire that can't be satisfied. Perhaps you could say "She has an insatiable desire to bankrupt me", but its not clear if this the case. Insatiable is often used for an unlimited desire for sex.
"Give an inch, take a mile" is someone who takes advantage of small kindnesses:
She asked if she could stay over for a night or two while she found a new place to live. But give her an inch, and she'll take a mile, and she's still sleeping on my sofa and helping herself to the contents of my fridge.
Since you are not being "kind" (you only pay what you must) it doesn't apply.
Simple terms for this behaviour include "greedy" or "money-grabbing".
A formal term is "avarice". It is a noun: "Her avarice is unlimited."
If her intent is to hurt you, rather than enrich herself, you could call her "spiteful" or "vindictive"