What’s the suggested step if your unit denies your emergency leave request while deployed? EO, IG... ?

Malignant cancer is not an emergency situation. Unless that member dies, you don’t have a reason for emergency leave. If you go on leave, when you return, the person will still have cancer so the leave had no effect.

I worked in the Mayor Cell on my last NTC rotation, and we received well over a hundred Red Cross messages in a few weeks. Some were things like “uncle diagnosed with cancer, death not imminent”. Your command is getting all these requests daily. Unless death is imminent, it’s not an emergency situation and doesn’t warrant emergency leave.

Not to be heartless, but I have to point out/ask.
Diagnosed is not the same as dying. Is there a timetable for life expectancy? Has that been presented as part of the request? If the family member was given 6 months (or even 3) to live, this would not qualify as an "emergency" in most people's eyes. I do not know what the reg says (and I am retired, so no longer have quick and easy access to look it up), but I would guess that it would agree.
I know this sounds cruel and unfair. But, provided that it is not TRULY an "emergency" situation (I.e. one week left to live), work with your NCOs to re-submit as an ordinary leave packet. Possibly even ordinary leave under emergency conditions (which is different than emergency leave, believe it or not).

Look, you are deployed probably OCONUS. The unit is the approval authority for all leaves. Immediate Family, is not the same as spouse/children. Diagnose is not always same as giving someone 2-4 weeks til death. You can visit higher CoC, but you probably will stay deployed.