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Unfortunately, you would likely not qualify for a compassionate reassignment due to the illnesses not being considered terminal and would not resolve itself in a period of 2 years. You can however volunteer for reassignment to Korea when your window opens

Soldiers may be considered for a compassionate action when they have extreme Family problems. The two types of Compassionate Requests are when personal problems are:

1. Temporary (resolvable within one year)

2. Not expected to be solved in one year

A compassionate action may be a request for reassignment, deletion, deferment or permissive attachment based on the soldier's circumstances.

Criteria and supporting documentation for Compassionate Actions are outlined in AR 614-200 Chapter 5.

AR 614-200 has all your answers. Note:

5–11. Criteria

c. Compassionate consideration will be given only for Family members. A Family member includes spouse, child,
parent, minor brother or sister, person in loco parentis, or the only living blood relative of the Soldier. Other persons, including parents-in-law, may also be considered provided they are documented as authorized Family members (see AR 600–8–14). If the problem is based on conditions of the parents-in-law, there must be no other Family members of the spouse's Family to help solve the problem.

5–12. Supporting documentation
The following documentation will be included (as appropriate) with DA Form 3739.
a. Medical problems. A signed statement from the attending physician giving the specific medical diagnosis, prognosis of illness, and treatment plan. The statement will include date of onset, past and anticipated periods of hospitalization, period of convalescence, and anticipated life expectancy for terminal cases. The statement will list any other factors that establish the Soldier's presence as having a bearing on the medical condition. For cases involving reassignment from OCONUS location where medical care for Family members is not available, include documentation from appropriate medical authorities stating that fact (see para 5–15g).
b. Legal problems. A signed statement from a licensed attorney stating the problem and the reasons why solutions other than reassignment of the Soldier are unacceptable. If applicable, a copy of court order, divorce decree, or other pertinent legal documents will be submitted.
c. Rape or child abuse. Statements from police, social service agencies, and/or examining physicians.
d. Marital and dependent status. When cases involve reassignment of Soldiers to dependent-restricted tours, a statement by the Soldier, witnessed by an officer, will be included. It will specify that the Soldier has been advised that travel for dependents at Government expense is not authorized.
e. Other problems. Supporting statements from responsible persons (for example, clergymen, social workers, court clerks, American Red Cross personnel) who have personal knowledge of.

Then keep on reading for temporary or permanent issues etc. It lists all the forms you need. You have to be very specific when it's medical.

I did a compassionate reassignment after my daughter got diagnosed with a genetic kidney disorder at 6 weeks old - that put her in the hospital twice by the time she was 4 months old. However, she got diagnosed in the state I grew up in, all my family and my then husband's family was there. And luckily was a spot for me at the joint assignment there. So I didn't have to renew the compassionate. Otherwise they're good for a year usually.

But read the AR. It should help.

Very unlikely since he is probably not listed as your dependent, and evidently you have been separated for quite sometime.