Various dynamical regimes associated with confined monopoles in the Higgs phase of N=2 two-flavor QCD are studied. The microscopic model we deal with has the SU(2)×U(1) gauge group, with a Fayet-Iliopoulos term of the U(1) factor, and large and (nearly) degenerate mass terms of the matter hypermultiplets. We present a complete quasiclassical treatment of the BPS sector of this model, including the full set of the first-order equations, derivations of all relevant zero modes, and derivation of an effective low-energy theory for the corresponding collective coordinates. The macroscopic description is provided by a CP1 model with or without twisted mass. The confined monopoles - string junctions of the microscopic theory - are mapped onto BPS kinks of the CP1 model. The string junction is 1/4 BPS. Masses and other characteristics of the confined monopoles are matched with those of the CP1-model kinks. The matching demonstrates the occurrence of an anomaly in the monopole central charge in 4D Yang-Mills theory. We study what becomes of the confined monopole in the bona fide non-Abelian limit of degenerate mass terms where a global SU(2) symmetry is restored. The solution of the macroscopic model is known, e.g., from the mirror description of the CP1 model. The monopoles, aka CP1-model kinks, are stabilized by nonperturbative dynamics of the CP1 model. We explain an earlier rather puzzling observation of a correspondence between the BPS kink spectrum in the CP1 model and the Seiberg-Witten solution.