Is there a word for the concept of not repeating your parents' mistakes?
Solution 1:
How about the idiom breaking the cycle. From The Free Dictionary:
break the cycle: To not participate in dysfunctional and/or unhealthy behavior. Often, such behavior is commonplace in one's family, and the person breaking the cycle does so to keep it from continuing through future generations.
This definition speaks directly to the concept of not repeating one's parents' mistakes.