Are there situations where it is wise to remove oneself from parents? My philosophy is to set an example to others though the path of a bodhisattva.
When offers of help are denied, one has done what they can. 
I'd say a temporary distance is acceptable in this situation. 

For the adult child of the sick one, maintain the intent to help and the compassion and bodhicitta for both parents. 

This is a rough time for all involved, in times like these emotions tend to cause conflicts that might seem to be about one thing,  but are actually about the emotions caused by the looming death of the loved one. 

To the adult child my advice would be as follows :

Try not to take things personally here.
Drop off care packages for both parents. 
Make sure to let it be known (in a positive way, text or short polite letter) that if you are needed you are a phone call away.
Do not worry about or mention next of kin.
Remember that others actions and words are not an excuse to "Water unwholesome seeds" 
Do not hold a grudge, and give yourself as much distance as you need. 
After the parent dies, if the remaining parent needs it, be there to comfort and ease the grieving process. 
Reread all the branch and root Bodhisattva vows, one by one, and ask yourself where you are doing well for each vow, and how you could improve on each vow. 
Remember that the vows apply to all beings, not just family. Treat yourself to some ice cream and some activities you enjoy. Spend time with friends. 

This kind of situation is an incredibly difficult one. For everyone involved. 
It can be trying and emotionally draining.
I do not know the full situation, only what is in the question. I've tried to keep this advice in line with the Buddhist tradition and Bodhisattva tradition to the best of my abilities. If there is some error please comment and I will edit accordingly. 

I hope this helps.