Q: Why are the Valar reluctant or unwilling to go to war against obvious evil? My question also implies that this needs to be explained in the film.
I agree that this question should definitely be addressed and discussed within the show. The Valar should raise a variety of points in their debate, Estel should ask questions, and Elrond should comment. We even have Bilbo giving his viewpoint on going to war in the final episode. This is something the audience deserves to hear addressed directly.
As for 'Why are the Valar reluctant to declare War?' - the answer is that the consequences of war are great. Large swaths of Arda will be utterly destroyed in a war between Melkor and the Valar, and they have to be well aware of this. Melkor's evil hasn't reached a level to justify that level of retaliation for most of Season One. He's more an inconvenient jerk than 'obvious evil' at this early stage. Who is he hurting, really? Where are the victims of his malice? Prior to the awakening of the Children....it's Yavanna's creatures, the lands of Middle Earth and his own followers. All will be much more damaged by a War than they are under Melkor, so.....
Melkor is redeemable. He could choose to join the Valar and help them to shape Middle Earth. He....does not make this choice. He (repeatedly) makes the opposite choice. But Manwë wants to give him every opportunity to make that choice. He knows that forcibly defeating Melkor and locking him up is unlikely to make that happen, and seeks to reconcile without constraining his 'brother.'
Q: Absolute good wins in war with any evil... These are not good in shades of white!
...And the Valar do win this War, handily. They are not afraid of losing (or at least, that fear has not been mentioned as a reason to avoid war). We could have Estel raise this possibility so that Elrond can discount it and mention their other, much more valid, reasons for not choosing to use force right away. Among other things, the word 'war' does not exist in their vocabulary yet.
Q: I can't think Tolkien would agree with the idea that war is intrinsically evil... he was not a pacifist.
No, he was not. He certainly wasn't one to wax poetic about the glories of war, either, though. His characters war out of necessity, and there are consequences to war which he does not gloss over. He has Merry chide Frodo that merely being 'shocked and sad' won't be enough to deal with the ruffians in the Shire. Even so, Frodo puts rather strict rules of engagement on the hobbits to prevent war crimes in the Battle of Bywater. Tolkien also mentions that healing among the elves was better carried out by those who did not kill (Aragorn's skill at both notwithstanding). Individual pacifism is not a bad thing in Tolkien's stories, as he has Frodo choose that over the course of LotR, even trying to refuse to carry a sword at the end.
As a devout Catholic, I would think that he more or less subscribed to Just War Theory:
http://plato.stanford.edu/entries/war/
Q: This is modern pacifism...
Addressed by others above. Just War theory states that war is just only when it meets certain criteria (defending against an aggressor and exhausting diplomatic solutions are two of the criteria that must be met). Failure to meet these criteria would mean that the war is judged unjust by classical Christian theologians (aka St. Thomas Aquinas). For a war to be considered 'just,' it must be launched for a just cause and right intention (no pretext). It must be declared publicly by a proper authority (ie, the state). War is meant to be a last resort, after diplomatic solutions have failed and all attempts to resolve the conflict without war were unsuccessful. There needs to be an evaluation of the consequences - can the war hope to achieve its intended outcome, and will the cost be proportional to the good you hope to gain? These are predictions, not 'known' quantities, but if you fail to take the consequences of your actions into account, it's not a just war.
Pacifism always concludes that war is the wrong answer. Just war theory does not always reach that conclusion, though it may conclude that many or most wars are, in fact, not just wars.
To apply just war theory to this conflict:
1) Manwë is the proper authority and has the right to declare war.
2) Diplomatic measures are implemented from the time Melkor enters Arda, and are increased in their forcefulness over time.
3) The destruction predicted to result from the war is too great to justify the intervention of the Valar until after Melkor's more grievous deeds come to light. (When the Elves awaken, that balance is tipped further).
4) Is the cause of the Valar just? Are they sure of that? I would say that they don't all reach that conclusion immediately. But yes, they do get there. Since 'just cause' translates to defending against an aggressor, they all have to eventually recognize that that is who Melkor is.