Your tripping that breaker because your load is too high on that circuit. The reason the breakers aren't tripping on the garage panel is that the load on those individual circuits aren't too much for that point in the circuit, but it's too much for the main coming out of your main panel. Picture one man holding up 3 people each holding 50lbs. While the individuals holding the 50lbs can handle the load, the one man trying to carry all 3 of the others is too much for him.


You really need to determine the draw on that circuit and modify the main panel accordingly. Too much load on a circuit with a failure to trip the breaker could be devastating. While it's been 30+ years since then, I had extensive residential wiring training but I know my limitations and won't attempt breaker panel work on my own. It's too easy to put my home at risk, violate local codes, etc.