Yes, we need pictures please.
Also, what thickness are the flexible cable conductors?
What are the brown squiggles?
Are you positive that wire you have coloured blue links the two switch positions?
The red/black wires...do they link the two switch positions?
As well as the pix, you may need to use a multimeter to check this. To do this, turn off the power and prevent re-energisation.
At one switch, join the red/black together. At the other switch, using the MM set to continuity setting, connect the red black to the MM's probes. If there is continuity, there will be a buzz or the meter will read 0.00.
At a guess, the red/black will link the switches. The blue wire you have drawn will not link the switches, but be 2 separate wires: a live feed at the 2 gang switch and a switchwire for the hall light at the 1G switch. My guess is that the red/blacks will go into the two lower terminals at the 1G sw and the blue wire in Common. At the two gang switch, the red/blacks go in the lower terminals again of the switch you want to operate the hall light. The live feed (which you will need to identify) will go in the Common, linked across to the Common of the outside switch. Finally, the outside light switchwire will go in one of the other terminals.
But this is purely my guess. Don't try anything until you have posted pix and done a bit of footwork with the MM.