Legacy of the Wizard © 1989 Broderbund Software, Incorporated.
North American release. Game developed in Japan. See the original Japanese version for more information; "Dragon Slayer IV - Drasle Family".
Description from the back cover:
Long, long ago, an evil dragon terrorized the forest until it was imprisoned by a powerful wizard. Now, years later, the dragon has revived and it's up to you to use the power of the wizard's descendants, the Draslefamily, to defeat the dragon once again.
The whole family takes part in this action adventure as the parents, children and even the family pet search huge dungeons for gold, keys, magic, hidden crowns and finally the magical sword that can destroy the dragon.
Click to enlarge