Wallace's problem is that Halleck did not like political generals, but he could be a bit kinder to Republicans and Wallace was a Democrat. For instance, Halleck liked Hurlbut, who just so happened to be of Lincoln's staunchest allies in Illinois. So Halleck cultivated Hurlbut. Grant after Fort Donelson and Shiloh purposely befriended Halleck friends and favorites (Sherman, McPherson, Hurlbut, Smith, Pope, Sheridan, Ord) to gain his approval. It worked over time although it remained a very strange and strained relationship. Halleck and Grant were FAR better at army politics than most give credit.
Wallace did not help his case by showing up at the Fort Donelson surrender discussion before Grant, who was very sensitive about being usurped. It seems to be an innocent mistake by Wallace, but Grant was noticeably cooler after that. To make it worse, Wallace complained to people who were friends with Grant about Shiloh. Another example of such bone-headed actions was Thomas Worthington. He hated Sherman and brought it up to Halleck, who played a large role in saving Sherman's career and promoting his actions at Shiloh. The ability to deal properly with the politics of war and build friendships with fellow officers was a skill men such as Wallace and especially Worthington did not master. One might call this unfair. I call it human nature.
Wallace was doomed. He was a Democrat serving a Republican administration that mostly undermined Democratic generals, lest they gain political capital. He was under Halleck who disliked political generals, particularly ones who gave him no advantage in his dealings with the Republicans who ran the government. He had none of the qualifications Grant prized, namely obedience and Halleck's favor. The last nail in the coffin was that his division suffered few losses on April 7. They were vital to victory bythreatening the Rebel right but no other division got off so light at Shiloh unless you count Thomas J. Wood's command. That might be where the coward comment came from. Wallace lost at most 300 men. Most of Grant's brigades lost more than that and three of Buell's brigades reported losses in excess of 300.
As to Wallace, I doubt he seriously considered going down the Shunpike to hit the Confederate rear. Owl Creek was sluggish but deep and it could be crossed at one bridge which was being guarded by the Texas Rangers (the best Rebel cavalry unit at Shiloh), and for time both the 38th Tennessee and Crescent Regiment and some artillery. Wallace mentioned considering it (but he apparently told no one at the time) but after the war he looked at the ground and said it would be folly.
That said I highly recommend Wallace's autobiograpghy. Its a great read but also very accurate at least about Shiloh. It lines up well with contemporary accounts and is still the best account of the fighting on the Union right on April 7 since it is vivid and detailed.