A way to use unhinged would be.
The babysitter become unhinged when the 2 toddler twin boys would not stop fighting and tore up the house.
It is okay to say unhinged.
However some people may be offended by the saying unhinged but people can get offended by anything.
There's really nothing wrong though with saying unhinged.
When you say that someone comes or becomes unhinged, you mean that they begin to behave in an uncontrolled or unreasonable way.
Unhinged is an adjective.
The adjective is the word that accompanies the noun to determine or qualify it.
If someone's unhinged, they aren't completely sane. Unhinged is another way to say "crazy" or "out to lunch."
Unhinged can also mean someone is mentally ill or has a mental illness.
Some synonyms of the word unhinged include.
deranged.
disturbed.
manic.
unbalanced.
confused.
crazed.
touched.
bananas.