I have no books to suggest, but a couple of comments.
I am puzzled as to why you find this puzzling. Having spent close to a century as the “third, centre party”, with considerably fewer seats than the Conservatives or Labour, the Liberals gave up hope of forming a government by themselves decades ago, but clung to the hope of a return to a measure of power if an election led to a hung parliament, with neither major party holding a workable majority. Finally, their dreams came true and they grabbed the opportunity with both hands. Of course, they should have known that it would be a poisoned chalice, but given that it was the only thing that had given the Parliamentary Liberal Party any raison d’être for many decades, they could hardly turn it down.
A coalition with Labour wold not have been viable even though many Lib Dem activists (though not so many Lib Dem voters, I suspect) would have been more comfortable with it. Even together, the two parties wold not have had an overall majority, and would still have needed to do deals with Celtic nationalist parties with which they have little in common. Furthermore, the electorate appeared to have fairly decisively rejected Brown’s Labour party, and the Lib Dems popularity would probably have plummeted even more quickly than it actually did if they had seemed to be “propping up” Brown. At least an alliance with the Tories could be made to look like a “new start” and, initially at least, like a real coalition which the Lib Dems had helped to shape. They really had no choice. in fact, their leverage within the coalition was very weak, and Clegg does not appear to have played the rather poor hand he was dealt at all skillfully, but that is another matter.
There was no time period between these things. One followed immediately upon the other.