This paper presents UMIRA (Unified Memory-Integrated Retrieval and Task Alocation), a framework that integrates personalized memory-augmented retrieval with large language model (LLM)-driven task allocation and execution planning for elderly care in smart home environments. UMIRA combines an episodic memory module, which preserves and leverages user-specific interaction history, with a domain-specific Retrieval-Augmented Generation (RAG) pipeline to provide contextually grounded responses. In parallel, a multi-agent coordination module decomposes high-level user requests into a list of executable subtasks, allocates them across multiple embodied agents based on skill and capacity constraints, and manages their execution while preserving inter-task dependencies. The framework is evaluated in the AI2-THOR simulation platform using a curated elderly care knowledge base, with experiments covering retrieval accuracy, response generation quality, and multi-agent task execution efficiency. Experimental results demonstrate that UMIRA outperforms baseline methods, delivering higher retrieval precision, improved semantic alignment in generated responses, and more efficient, coordinated agent utilization. These findings highlight the potential of integrating personalized memory retrieval with LLM-based planning to enable adaptive, scalable, and user-centric assistance for aging-in-place scenarios.