The sentiment of wanting to die first has me the most confused. The woman is an adult and thus better at understanding/dealing with trauma. If she died first, Ink would be beyond devastated. Whatever the heck is going on in this comic, wanting to subject a child to tragedies they're unequipped to deal with hints at a relationship that's less than stellar.
Perhaps if the woman died first, she would be freed from her obligation to resurrect Ink again and again.