Quantum coherence is one of the significant properties of quantum systems, and it is widely used in the quantum information processing and condensed matter physics. An important research topic is the correlation between the quantum coherence and the quan-tum phase transitions in the many-body system. However, most of the previous works mainly focused on the total coherence of quan-tum system, and the detection of quantum phase transitions can be hindered by some physical effects. It is well known that the total coherence and its distribution are closely related but also have their own unique properties. In order to overcome the failure of the detec-tion, it is necessary to investigate the ability of coherence distribution to detect the quantum phase transitions and the impact of some physical effects on the detection. Moreover, how to regulate and control the coherence decomposition of a quantum system is very important for performing quantum information processing tasks. Whereas, the current researches cannot give a satisfactory answer. In this work, it is chosen as the research object that two-spin system surrounded by a one-dimensional XY spin chain with a Dzyaloshinsky-Moriya (DM) interaction. Based on Jensen-Shannon entropy, the coherence distributions (localized coherence and collective coherence) and their critical behaviors are investigated. By changing spin-spin coupling and DM interaction, the con-trol of quantum coherence components in a two-spin system has been achieved. The strong spin-spin interaction increases the col-lective coherence of the two-spin system and reduces its localized coherence. The strong DM interaction increases localized coherence and reduces collective coherence. In addition, the localized coherence and collective coherence of the two-spin system can accurately characterize the first-order quantum phase transition through local extremums, but the spin-spin interaction and DM interaction seriously limit the accuracy of localized coherence in characterizing it. The first derivative of local coherence and collective coherence can accurately characterize the second-order quantum phase transitions through divergent behaviors, and is not affected by spin-spin coupling and DM interaction. Finally, it is found that the total coherence and collective coherence of long-distance spin pairs can accurately characterize first-order and second-order quantum phase transition through their critical behaviors. Especially for second-order quantum phase transition environments, the longer the lattice distance between spins, the more significant the critical behavior of the two types of coherence.