While Large Language Models (LLMs) have shown remarkable advancements in reasoning and tool use, they often fail to generate optimal, grounded solutions under complex constraints. Real-world travel planning exemplifies these challenges, evaluating agents' abilities to handle constraints that are explicit, implicit, and even evolving based on interactions with dynamic environments and user needs. In this paper, we present ATLAS, a general multi-agent framework designed to effectively handle such complex nature of constraints awareness in real-world travel planning tasks. ATLAS introduces a principled approach to address the fundamental challenges of constraint-aware planning through dedicated mechanisms for dynamic constraint management, iterative plan critique, and adaptive interleaved search. ATLAS demonstrates state-of-the-art performance on the TravelPlanner benchmark, improving the final pass rate from 23.3% to 44.4% over its best alternative. More importantly, our work is the first to demonstrate quantitative effectiveness on real-world travel planning tasks with live information search and multi-turn feedback. In this realistic setting, ATLAS showcases its superior overall planning performance, achieving an 84% final pass rate which significantly outperforms baselines including ReAct (59%) and a monolithic agent (27%).