Add a CD4013 flip-flop.But it doesn't meet the criteria defined by the TS. i.e. double click = latch on, single click = off.
The switch input pulse clocks the flop with an '0' on the data line- this resets it, the output of the double-click detector goes to the SET input.
The SET input persists long after the bounces die down, so it would stay SET.