Exactly. Theoden's first destination was the Fords of Isen to help with the battle there. But he is diverted to the Hornburg by Gandalf after they come across those fleeing from the battle at the Fords.
Also on the March 2, and unknown to Saruman, Gandalf reappears from beyond death and rehabilitates Theoden. Theoden immediately marshals his forces and sets out for the Westfold. I need to check, but as I recall, I don't think Theoden immediately heads for Helm's Deep. I think he originally intends to support the forces at the Fords but heads for the Hornburg after messengers come with word that the Fords were taken.
This, for me, is one of the biggest points and you did a good job expressing it. Battle then was not like it was now.If something happens in a battle even half way across the world the important people know about it almost instantly. This was simply not the case then. If a king was not at the battle he might not know what happened for hours, perhaps even days. And even if he was in one part of the battle it does not mean he did not know what was happening elsewhere. This is why kings gave their battlefield commanders a lot of power.
Were Saruman and his lieutenants aware when the White Hand forces set out that Theoden was headed for Helm's Deep? How fluid was the situation after they won the Fords of Isen? In any case, I don't think we can make definitive assumptions about what orders Saruman gave his commanders on March 2. Remember that Merry and Pippen (with Treebeard and the ents) watch Saruman's armies march out of Isengard. Shortly thereafter they assault Orthanc, and we can imagine that Saruman is thereafter preoccupied and has limited contact with his army in the field. I think that the White Hand forces pursued the survivors of the Fords as they fled to Helm's Deep and probably were not aware of Theoden's relief force until the White Hand forces drew near to Helm's Deep. Even if they were aware, they may have been trying to reach it first in order to cut Theoden off, which would have been disastrous for Theoden. Even with perfect information, I think that it would have been reasonable for the field commanders to decide that the best course of action would be to engage and destroy Theoden's forces rather than to divert to Edoras and leave Theoden in a strong position at their back. As it played out, it was very nearly the right decision. The White Hand forces defeated Theoden at Helm's Deep. But for the highly improbable arrival of Gandalf (an Istari) with a relief force that included Eomer and the other scattered survivors of the Fords, Theoden was doomed. Actually, even with the arrival of Gandalf's relief force, I believe that the White Hand would have prevailed at Helm's Deep but for the completely unimaginable arrival of a hostile huorn tree army during the night.
Yes, yes I agree completely. Saruman made the only throw open to him but fate, providence, wryd whatever you call it stepped in. Wyrd is never something can plan a sound strategy on, since you cannot predict it and often time by trying to achieve it you simply work against it. But when it does come... well as you see with Saruman, and even Sauron, it can undo the best laid plans in a heatbeat. The eucatastrophe was, in my own opinion at least, one of Tolkien's greatest ideas. And what happens with Saruman is a case study in it.
Lastly, I want to return to the point I made in the old post excerpted above. At this point Saruman was in a terrible position vis a vis Sauron. Saruman's only true hope of victory was to sieze the Ring first. There were two possibilities. Either Merry and Pippen had possessed it, in which case it was lost somewhere in the vicinity of Fangorn and he needed a free hand to search for it. Saruman might also reasonably conclude that on or about March 1 there was a risk that the Ring was in the hands of a champion of Rohan. If so - if Theoden or Eomer had the Ring - he had to kill them before they learned how to use it. The other alternative is that the Ring was still somewhere in the vicinity of the Anduin and headed for Minas Tirith. In that scenario he needed a free hand to hunt for the Ring bearer all the way on the far side of Rohan. I don't think Saruman would have felt that he could afford to leave Theoden and an army of Rohirrim at Helm's Deep. I think Saruman had no choice but to play for an immediate crushing victory. In the grand scheme things, Saruman's victory over Rohan would be meaningless if the Ring escaped him. He could never hope to defeat Sauron's forces without it. I think Saruman made a sound decision both tactically and strategically, but was undone by a few unlikely twists of fate.
He wasn't the only one. I don't think Sauron made bad choices. If Eowyn doesn't kill the Witch King, Gondor falls and Sauron wins. If Aragorn doesn't walk the Paths of the Dead and rally the Oathbreakers, Gondor falls and Sauron wins. If a hobbit and his servant don't walk alone into the most inhospitable and heavily guarded place in Middle Earth, all the way to Mt. Doom while evading capture, starvation, etc., Sauron wins. If Sam doesn't go into full Terminator mode and defeat Shelob, Sauron wins. Even with all of that, Frodo actually fails. At the final test, he can't find the strength of will to destroy the Ring.
Ultimately, it is only by the grace of Illuvatar that the light prevails and Sauron is defeated. That is not to denigrate the role of the heroes of the story. Their courage and sacrifice are in a sense the vehicles through which the grace of Illuvatar is made manifest. Without Frodo's very nearly indomitable will, he does not make it to the precipice for his encounter with Gollum. Without Frodo's pity, Gollum does not survive to the encounter. But for Faramir's wisdom, Frodo does not leave Ithilien with the Ring. But for actions of Aragorn and Eowyn, Gondor is defeated and Sauron is not distracted at the critical moment.
All of which is a very long winded way of saying that I disagree that Saruman made a foolish tactical decision to assault Helm's Deep.