Any inquire at RAHS requires a PRIVACY RELEASE.Call your nearest Ukrainian Consulate or Embassy and tell them you would like to obtain Mama's birth certificate on her behalfand ask what is required of you to obtain it. They might ask you to include copy of one of her Australian documents. Don't forget to includeher full name and her birth date. Then copy address as above.
Summer is not a good time to make inquiries.All archives are busy with tourists and August is govt holiday time, so many are already daydreaming about their vacations. Prepare what you need to now and then second week of September send out your inquiry.
Once you have documented some more info, I can put you in contact w/someone in Lviv, who can make some phone calls for you etc.
Don't get anxious.Be patient.If there is surviving family, you will find them.And don't forget you may also have family in Poland.One has to do this all one step at a time.