Not being funny but it sounds like they are in a worse situation than you they have no 1 in-line who knows what there doing by the sounds of it. Your expected to show the other guy what to do right?
If it was me i would be telling them what i was doing If i was you mate i would go out with the extra money i assume you have earned from all the other time and go and book a 2 week holiday with the family.
Take a copy of the holiday dates to HR hand it to them and say ill be off those dates and walk out.
What can they do fire you? for what? there only going to leave themselves short on staff who have no clue what to do then there buckle under pressure and they will have no 1 :D