I honestly don't get why you would think the Lib Dems and Tories were diametrically opposed, though. If you read the manifesto, read speeches etc. it's obvious that there was a fair bit of common ground with at least part of the Tory party, despite the obvious differences.
I think the problem is that a lot of people just projected on to the Lib Dems what they wanted the party to be, regardless of what the party actually said. There was this perception that the Lib Dems were to the left of Labour, which wasn't true.
Re. what influence the LDs have had in government - you just need to look at the list of Tory complaints to get an idea of that. Capital gains tax increase (remember how the Telegraph fought that), keeping out the inheritance tax cut, keeping out the marriage tax break, keeping the 50p rate as longfingernails pointed out, introducing increase in tax threshold, Danny Alexander now pushing for no tax cuts during this parliament, no hardline policy against the EU, Ken Clarke's prisons policy wouldn't have appeared in a Tory minority govt., etc. The LDs got the threshold for immunity from public sector pay freezes cut. Human Rights Act staying (which is a major victory, for now anyway). And the AV referendum. Pupil premium (although this was partly Tory policy too?)
Obviously I could also make a list of what I'm not happy with, but the LDs make a fair amount of difference (ask John Redwood).
And there's a lot that's agreed on, and not just by some Clegg cabal, as people like to paint it - things that the centre of gravity of the party are behind.
Re. forcing a new election - that would have been completely irresponsible in the financial climate.