Chromatin fibers within the interior of the nucleus of the cell make stable interactions with the nucleoskeleton， an ensemble of ``extra-chromatin'' structures which help ensuring genome stability. Although the role of these interactions appears crucial to the correct behavior of the cell， their impact on chromatin structure and dynamics remains to be elucidated. In order to tackle this important issue， in this work we introduce a simple polymer model for chromatin fibers in interphase which takes into account the two generic properties of chain-vs.-chain mutual uncrossability and the presence of stable binding interactions to an extra-chromatin nuclear matrix. To study how these constraints affect chromatin structure from small to large scales， we employ extensive molecular dynamics computer simulations and we monitor the motion of nanoprobes of different sizes embedded within the polymer medium. Our results demonstrate that nanoprobes show hampered motion whenever their linear size becomes larger than chromatin stiffness. This transition is also displaying features which usually belong to the realm of glassy systems， namely long-tail correlations in the distribution functions of nanoprobe spatial displacements and heterogeneous behavior accompanied by ergodicity breaking.