Forum rules do not allow us to provide ?how to? assistance to a person who does not work in this industry. But we are allowed to answer ?how come? questions. So I am reopening this thread just long enough to provide that answer.
It is not that you have a problem between the two panels. It is that you have an unrealistic expectation of how breakers do their job. The fact that the number 60 is smaller than the number 100 is not enough to ensure that the 60 amp breaker will trip, instead of the 100 amp breaker, when a fault takes place somewhere downstream of the two. If there is arcing and sparking on a 20 amp circuit, then there could be hundreds of amps flowing, or even thousands of amps. Those amps will flow through all three of the breakers (i.e., the 20, the 60, and the 100). Within all three breakers the trip mechanism will be actuated. Why should you expect that the 20 will trip, or the 60 will trip, instead of the 100, when all three are seeing a huge amount of current?
In order to prevent future occurrences of this type, you would have to have a professional engineer perform a ?selective coordination study.? Then you would have to follow that person?s advice regarding replacement of certain circuit breakers with certain others, so that there can be an intentional delay in the tripping of the upstream breakers, thus giving the downstream breakers a chance to trip first.