I'm not thinking you are correct on this....exercising an option at $4 just establishes your holding period on the stock and (if held) will cause no capital gain, it will just establish the date of acquisition... until it is eventually SOLD...short term or long term at that point in time!
ISO are incentive based options and are taxed at cap gain rates when sold if held for at least 1 year.
NSO are taxed as ordinary income at the time of purchase based on the difference between the option grant price and the exercise price. The gains are subject to income tax, Medicare tax and SS payroll tax.
I didn't look at how her options were granted to see what applies in her case.