We present a generalized r-adaptive deep learning framework for solving Partial Differential Equations (PDEs) on unstructured grids. While our previous work [1] demonstrated the potential of optimizing node locations using the Deep Ritz Method, it was constrained by the requirement of symmetric positive-definite operators and restricted to tensor product meshes. In this study, we overcome these limitations by introducing a First-Order System Least Squares (FOSLS) formulation combined with a fully differentiable Delaunay mesh generator implemented in JAX. The FOSLS approach reformulates the PDE as a system of first-order equations, minimizing the L2-norm of the residuals. This allows the method to robustly solve non-self-adjoint problems, such as convection-diffusion equations, while simultaneously providing accurate approximations for both the solution and its flux. The differentiable mesher enables the topology to evolve dynamically during training, concentrating degrees of freedom in regions with singular behaviors or strong gradients. To ensure numerical stability, we augment the loss function with a mesh-quality regularization term that prevents element distortion and employ a grid continuation strategy. This curriculum learning approach progressively refines the mesh by seeding new nodes in high-error regions, effectively mitigating the optimization difficulties associated with initializing dense, mobile meshes. Numerical results show that this architecture significantly outperforms fixed-mesh baselines and standard adaptive schemes in both accuracy and convergence speed. [1] A.J. Omella and D. Pardo. r-Adaptive deep learning method for solving partial differential equations. “Computers & Mathematics with Applications”, Vol. 53, pp.33--42, 2024.