Quagmire

From ''The Lemony Snicket Wiki''

Quagmire is the surname of Duncan, Isadora and Quigley along with their parents. It literally means a swamp, but is to be interpreted here metaphorically as a difficult or precarious situation.

[edit] Family tree

Quagmire father (deceased) -- m -- Quagmire mother (deceased)
                              |
                              |
            -------------------------------------
           |                  |                  |
        Duncan             Isadora            Quigley

Duncan and Isadora Quagmire got lost in a self sustaining hot air balloon. Quigley was said to be killed in the fire that killed the Quagmire parents and home but was actually alive and survived the fire.