Simulating nuanced human social dynamics with Large Language Models (LLMs) remains a significant challenge, particularly in achieving psychological depth and consistent persona behavior crucial for high-fidelity training tools. This paper introduces TACLA (Transactional Analysis Contextual LLM-based Agents), a novel Multi-Agent architecture designed to overcome these limitations. TACLA integrates core principles of Transactional Analysis (TA) by modeling agents as an orchestrated system of distinct Parent, Adult, and Child ego states, each with its own pattern memory. An Orchestrator Agent prioritizes ego state activation based on contextual triggers and an agent's life script, ensuring psychologically authentic responses. Validated in an educational scenario, TACLA demonstrates realistic ego state shifts in Student Agents, effectively modeling conflict de-escalation and escalation based on different teacher intervention strategies. Evaluation shows high conversational credibility and confirms TACLA's capacity to create dynamic, psychologically-grounded social simulations, advancing the development of effective AI tools for education and beyond.