Unfortunately, although I share your disgust, it is perfectly acceptable in our constitution for the party of government to change its leader (and hence the PM) without going to the country. Both parties get on their high horse when the other does it, albeit the tories were the last to say it is 'wrong' for labour to give us a PM who was not 'elected' (Brown); on this and the previous occasion labour have simply demand that we have a GE because the tories are shit.
That said, if Thick Lizzy is ousted it would be unprecedented - no party of government has booted out two of its own leaders in one term of office before.
(My preference would be for the dissolution of parliament and a general election within 3 weeks. Unfortunately this won't happen).
A couple of years ago we didn't have a government in Sweden for about five or six months. I swear that the air was fresher, the birds were louder and the weather better during those months.
Just dissolve the parliament. No need for new election.