Beorhtnoth at Maldon ~ Gandalf at Khazaddûm

[William Cloud Hicklin]

The battle of Helm's Deep is a direct result of Grima having borne word to Saruman of The Mark being revivified by Gandalf; except that Grima doesn't arrive at Isengard until after Saruman has send out his army and been captured by the Ents

Those are two contradictory statements: as indeed you say, Grima didn't reach Isengard until afterwards.

In the Battles of the Fords of Isen Tolkien gives a strategic overview of this period, and it's plain that the invasion of Rohan was long-planned. Saruman 'erred' in not launching it immediately upon Theodred's death in the First Battle; but his forces had taken heavier casualties than expected, and Grimbold's and Elfhelm's Riders were still in good order. At any rate the principal goal of the first attack was to kill Theodred. In the event, of course, the Second Battle occurred on the same day as Theoden's healing, so Grima could have had nothing to do with launching the invasion.

NB: Tolkien's time-synching slipped here. In the narrative, the Ent-borne Merry and Pippin reach Isengard in time to watch Saruman's army march out; but in Appendix B they arrive at night on the same day the Second Battle had already been fought!