Further to what Mark said, you could probably use a Worksheet_Change event in the two source sheets to send the data to the relevant destination sheets. You could use a separate criteria (such as, to be original, OK) so that you only send the individual rows of data that you want to the destination sheets.
From here (the destination sheets), using the same criteria brought over from the source sheets, you could send the relevant data to the Master sheet.
As for clearing the data from the Available Equipment/Mobilised Equipment Sheets, the code that you have in Module 1 (MoveStuff) will do that each time that you run that particular code. This line in that code:-
clears these sheets prior to any new data being transferred across.
Just an idea for you to ponder.