You can go through the US twice only if one is a transit between South America and another continent. You are not transiting to/from SA.
Thus, your route could be GIB (not GIG)-LHR-DUB-LAX-MEL-SYD-HKG-LHR-GIB as you must end your ticketed trip in GIB, not DUB. You could take a chance and throw away the LHR-GIB segment and buy a separate ticket home from LHR. Note that you cannot ticket ...HKG-LHR-DUB-LHR-GIB as you would have one too many segments in Europe.