Would like to know it too. I don't think I've heard about any established sort of exchanges there so best bet would be finding someone who is into it and exchange person to person
Regarding banks, their family should look into another bank.. there are very few banks that deal with USD on consumer level if any, Pumb Bank (
www.pumb.ua) is one that even lets you take out USD from their ATMs but shhh don't tell anyone
Privat bank as far as I know used to offer USD accounts but don't know if that changed
(could be that foreign currency accounts may not be available to end users but businesses should be having that option). A person can register as small biz entrepreneur entity (чacтный пpeдпpинимaтeль) which has its own tax benefits in comparison to other business licenses and can act as a normal business and be able to open USD currency saving/checking bank account that way if non avail. to general public )
Local currency there is artificially stabilized, that much I know about it. They want people to use local currency as much as general public likes to hold on to USD & EURO and I can only guess government has a deficit of USD since they don't want banks to put it out in circulation much. Ironically there are USD/EURO/UAH exchanges almost on every corner in big cities, or at least used to be that way few years ago.