But the Alliance is just that, an alliance. And now broken. Did the other parts of the alliance know of this splendid plan?

As I read it, yes. And that would be the basis for why they presented a common budget in the first place. The minor parties on both the left and the right usually use the seperate budget motions to raise their profile, which otherwise tends to be over-shadowed by the large party.

And the Alliance is not dead, it is just resting. Essentially it was a rebranding of the term Borgerliga partier, in effect "Bourgeoisie parties" or the non-socialists that the parties to the right of the Social Democrats has been using since at least the 70ies.

IM:

And why should the Swedendemocrats just play along?

Because their financiers are right wing and they voted something like 90% with the right wing government under the last parliament. The assumption was that the Sweden Democrats would be trapped, with their anti-socialist rethoric - culture Marxists with their PC crap keeping the ordinary (white) man down etc - they could not side with the socialists. The assumption was wrong, but not unreasonable.