As Raumar points out, the correct spelling is Sen somnar båda två bums i kanalen!
The phrase as a whole is not an idiom, but the part bums i kanalen is. Bums is a colloquial word, first attested in the 18th century and said to be of Low German origin. Nowadays it is only used in the meaning ‘at once’, but in the 19th century it often meant ‘straight (in a particular direction)’. The expression bums i kanalen is (was) therefore a humorous way of saying ‘straight into the canal’.
As the story goes, during festivities to celebrate the opening of Göta Canal in 1832 many people got drunk, and some of them ended up in the canal. This is said to be the origin of bums i kanalen. In actual fact, these three words together appeared on print at least as early as the previous year, but the canal incident may have popularised the expression.
Bums i kanalen is rarely used nowadays and largely appears to have lost its literal meaning. People tend to use it to mean simply ‘immediately’ or even just to say ‘Hurry!’ To me, the quoted sentence means ‘Then they both fall [or fell] asleep straight away’. (The choice of present or past tense depends on the context.)