Smart home automation increasingly relies on user-defined rules across heterogeneous IoT devices. While these rules appear harmless in isolation, their concurrent execution creates hidden, cross-rule interactions via shared devices, environmental variables, and physical topology. These interactions result in unsafe, wasteful, or privacy-threatening behaviors that are completely invisible to text-only analysis. Existing conflict detectors remain siloed, catching either static syntactic conflicts or specific environment-mediated interactions without unifying the two or providing actionable repairs for non-expert users. This paper presents SHACR, a smart home conflict resolution framework that anchors Large Language Model (LLM) unpredictability by grounding its reasoning in a formal, directed knowledge graph. SHACR encodes devices, capabilities, physical states, and Trigger-Condition-Action rules as typed, traversable entities. By elevating physical cause-effect relationships to first-class graph edges, SHACR transforms conflict detection from fragile text inference into deterministic multi-hop graph traversal, unifying logical, semantic, and physical conflict classes. It drives a closed-loop Scan-Explain-Repair-Validate workflow that uses the graph to bound the LLM's action space. We evaluated SHACR on a testbed of 203 rules deployed across 70 apartments within a smart building. By holding the underlying LLM fixed and introducing SHACR's knowledge graph, classification errors drop by 36.7\%, F1 rises from 0.59 to 0.79, and few-shot calibration further lifts F1 to 0.95, whereas the same calibration barely helps a graph-free LLM. Ultimately, this work challenges the current AI paradigm, establishing that structured knowledge representation is a far more critical factor for dependable IoT automation management than prompt engineering or underlying model architecture.

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