Should I hold the fort when HT and DHT are absent?

You could look at it as good experience, keep notes of what you do and use the examples in the interviews you will get when you apply out.
Or you could ask for a proper system of cover where everyone with a responsibility has to take their turn or the responsibilities are split up in some "fair" way.
Some people would be glad of the opportunities though, in spite of the frustration. In my experience , in teaching first you do the job then you get the recognition.

 

Does your school not have any agreement on who is in charge if the HT & DH are not there? In our staffing information, there's a section which states exactly when it would be my turn to be in charge (it happened one afternoon last term!)