CholeskyQR2 for Ill-conditioned Matrices (CholeskyQR2-IM) is a modern C++ library designed to compute the QR factorization of extremely ill-conditioned tall-and-skinny matrices. It is based on the Cholesky QR2 algorithm, which is widely recognized for its performance and ease of parallelization on distributed memory systems. The CholeskyQR2-IM presents an alternative approach that combines the traditional CholeskyQR2 with the shifting technique and the modified Gram-Schmidt process. The innovative approach improves both the numerical stability of the algorithm and the accuracy of the calculated factor Q. The library is specifically designed for QR factorization of large tall-and-skinny matrices on distributed memory systems and provides full support for both GPUs and modern CPUs.