Recovery is different with every case. It depends on how sick the person was.
Just because someone is sick and is hooked up to tubes does not make them "emotionally incompetent"! Would you tell a kidney dialasis patient or any other physically ill person that they must be "emotionally incompetent" just because they are hooked up to tubes? To me that is very poor logic on your part.
The point that was put forth was that Allison was under duress and coerced. She was coerced and under durress not just because she was physically ill. Either the lawyer, "friend", or "adoptive family", (or all parties), used her condition to unethically put in progress the adoption. She was held in the lawyers office to further strain her physical and emotional state so that she would become even more strained and compliant.
Would you ask ... "How long does it take someone to recover from cancer, a heart attack, or a back injury?" You probably would not because you would be able to surmise that the length of recovery would depend on the severity of the case. Also, how much help you have and how much rest you are able to get can affect your recovery... as can whether or not you have good nutrition.
Allison's case was severe, and with little help in trying to care for twin babies, she was assuredly sleep deprived. Also, her nutrition was still insufficient and her condition continued to deteriorate. She did not have key components that are necessary in order to progress recovery.
To be more specific about HG post-partum recovery time, here is a link for you to look at
http://www.helpher.org/mothers/postpartum-recovery/index.php
and here is a quote from that link:
"Recovering from hyperemesis gravidarum (HG) can take a few months or as long as two years. It will often take 1-2 months of recovery for every month you were ill. Women who have nausea/vomiting into late pregnancy usually find it takes several months to regain their energy and restore their nutritional reserves. "
The time at which Allison signed the papers was 5 weeks post-partum.
You posed a very excellent question when you wrote this "are hospital staff not trained to deal with this?"
To answer that, no... many health professionals are ignorant of this disease or misinformed.
Unfortunately, the severity of HG does not always depend on who your Dr. is, and even if you have an excelent Dr., you can have a severe case of HG. ... Again, just like with any illness.