Final answer:
The division of the nucleus where replicated chromosomes are distributed to two daughter nuclei occurs during anaphase of mitosis.
Step-by-step explanation:
The division of the nucleus you describe takes place during mitosis, which is a process with four main phases: prophase, metaphase, anaphase, and telophase.
Anaphase is the phase during which the replicated chromosomes, consisting of two sister chromatids, are separated and pulled to opposite poles of the cell. This ensures that each of the two resulting daughter nuclei receives an identical set of chromosomes.