They were against each other insofar as they both wanted the Ring of Power and both wanted to defeat the other, but they were cooperative because they both felt the threat of the 'good guys', particularly Gondor. They didn't like each other but they hated Gondor more.
I think it's sad how the film shows Saruman as being, like you say, a puppet and little more.
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Los Ingobernables de Harlond
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