This work presents a decentralized optimization conflict resolution method based on a novel Alternating Directions Method of Multipliers (ADMM) variant and model predictive control (MPC). The variant, titled Online Adaptive Alternating Direction Method of Multipliers (OA-ADMM) aims to unify the application of ADMM to online systems, i.e. systems where fast and adaptive real-time optimization is crucial, into one framework. OA-ADMM introduces two user-designed functions: the similarity function (a forgetting factor between two time steps of the online system) and the adaptation function (adjusting the penalty parameters between updates). The similarity function is what allows OA-ADMM to be applied to online systems where conventional optimization is too slow; the adaptation function allows the user to adjust the online feasibility of the system. We prove convergence in the static case and give requirements for online convergence. Combining OA-ADMM and MPC allows for robust decentralized motion planning and control that seamlessly integrates decentralized conflict resolution, instead of using separate subsystems or hierarchical optimization. The additional robustness is achieved by using the adaptation function of OA-ADMM as an additional safety measure, allowing the prioritization of certain constraints for (nearly) unsafe states, whilst the similarity function allows optimization at the desired control frequency. This method is compared with convention ADMM in Matlab, resulting in significant improvements in robustness and conflict resolution speed. Finally, we compare our OA-ADMM and MPC based decentralized conflict resolution method against conventional decentralized conflict resolution methods in the CARLA vehicle simulator. The results show that the OA-ADMM based method has improved performance, safety, robustness, and generality compared with traditional methods. The method also has fewer requirements in terms of prior knowledge (e.g., the geometry of the intersection), making it usable in almost any situation.