From Omega Vintage Database:
Ladymatic Ladies' leather strap
Reference ST 566.0001
International collection 1965
Movement Type: Automatic (mechanical)
Caliber number: 681, 24 jewels
Central sweep second hand.
Created in 1963
Functions Date
Case Stainless steel
Case back Press-in
Dial With hand-riveted solid gold hour markers and “bâton losange ” hands.
Crystal Armoured hesalite
Bracelet Leather
Water resistance 30 meters
As for your watch value, unfortunately vintage ladies watches' market is very thin. USD 100-200 would be my best guess if you can find a buyer.
I would suggest you take it to a qualified watchmaker near your place (not necessarily Omega since it will be bit expensive), and have it clean and lubricate. Your wife could cherish it because (A) it is a gift from her beloved aunt (B) it is a successful and famous Omega line during its time.