An unemployed mother works hard to get an honorable job as a zookeeper, but then finds herself at the center of an ethical conflict between a zoo and an unorthodox shelter for wildlife.

Is it absolutely important for us to know that she is unemployed? Obviously it won't matter anymore seeing as how she gets the job. ?I am also not clear on who the antagonist: is it her employer (the zoo)? Or is it another zoo and the shelter?

I would write it like this:

"An inexperienced zookeeper must fight for animal rights when she discovers unethical practices from her new employer and a shelter before a rare elephant is killed"

I would drop the first part of the logline because as written you have two inciting incidents.

The first inciting incident is getting the job, the second inciting incident is discovering she is the center of an ethical conflict
Since the ethical conflict seems to be the story, begin the logline there not how she got the job.

Agreed with the above comments.

As a rule of thumb, loglines are made up of clear details, not vague statements. Therefore descriptions such as "...an unorthodox shelter..." are not helpful in a logline.
These kinds of descriptions could mean anything, for example, they could give all the animals massages after being fed - that's unorthodox...
Obviously, you mean they are doing bad things to the animals, but that could also mean any number of things - medical experiments, inhumane living conditions, systematic euthanasia.