This study introduces an Inclusive AI Interaction Framework designed to enhance happiness, emotional well-being, and compassionate digital care through the integration of emotion-aware algorithms, adaptive conversational models, and accessibility-centered interface design. The framework prioritizes inclusivity by addressing diverse user abilities, cultural backgrounds, and emotional states, ensuring that AI interactions remain fair, empathetic, and supportive for broad user groups, including vulnerable populations. The study aims to examine how personalized and affectively responsive AI interactions influence emotional comfort, perceived empathy, trust, satisfaction, emotional stability, and sustained engagement among diverse users. A quantitative research design was employed, using structured questionnaires, multimodal sentiment-based rating scales, and standardized World Health Organization WHO-5 well-being measures to evaluate user well-being. SEM was applied to validate the relationships among core constructs and assess the impact of inclusive AI design on affective outcomes. The analysis revealed significant positive effects of inclusively designed, emotion-sensitive AI systems on affective outcomes, including trust, satisfaction, emotional stability, and overall emotional comfort. The findings demonstrate that inclusively designed, emotion-sensitive AI systems can meaningfully elevate user well-being. This research provides empirically grounded design principles and practical insights for developing emotionally supportive, ethically aligned, and universally accessible AI solutions that contribute to more humane digital experiences.