Dig to Australia - antipodes
MATL, 51 bytes
'NS'tPXEii'WE'tPXE648e3i60:qXJZA-JYAtn3-?2:&amp;)wJZAwh

Input format:
'N'
[50 26 23]
'W'
[4 18 29]

Output format:
S
50 26 23
E
175  41  31

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Explanation
'NS'tPXE     % Take input (string) implicitly. Exchange 'N' and 'S'
i            % Take input (array)
i'WE'tPXE    % Take input (string). Exchange 'W' and 'E'
648e3        % Push 648000
i            % Take input (array)
60:qXJ       % Push [0 1 ... 59]. Copy into clipboard J
ZA           % Convert second input array from base 60 to decimal
-            % Subtract
JYA          % Convert to base 60
tn3-?        % If length exceeds 3
  2:&amp;)       %   Split into first two elements and then the rest
  w          %   Swap
  JZA        %   Convert from base 60 to decimal
  wh         %   Swap, concatenate