The phase transition from the kinetically favored tetragonal form II into the thermodynamically stable hexagonal form I is the general phenomenon and core issue in application of polybutene-1-based materials. It is known that the variation of molecular structure by copolymerizing counits and the imposition of external stretching both greatly affect the phase transition. In this work, a series of butene-1/4-methyl-1-pentene (4M1P) random copolymers were synthesized with the dimethylpyridylamidohafnium/organoboron catalyst, where the 4M1P incorporated is the counit type of depressing II-I phase transition. Mechanical tests were combined with the in-situ wide-angle X-ray diffraction (WAXD) method to study the competing effects of the presence of 4M1P counits and stretching on the II-I phase transition. First of all, the quiescent experiments reveal that addition of 4M1P counits not only slows down transition kinetics but also decreases the ultimate form I fraction in the transition plateau. The 4M1P concentration >= 3.40 mol % is high enough to completely impede the II-I phase transition even when the aging time is as long as 4 months. Second, the stretching-induced phase transition was explored with the combined structural and mechanical information from WAXD and mechanical characterizations, respectively. The influence of stretching stimuli in the phase transition varies with 4M1P concentration. For low 4M1P concentration <= 1.00 mol %, stretching significantly accelerates the transition kinetics and induces the complete transition of form II. For intermediate 4M1P concentration 3.40 mol %, stretching effectively triggers the occurrence of the II-I phase transition, which does not start under quiescent conditions but only induces partial transition until fracture. For high 4M1P concentration ranging from 7.80 to 30.1 mol %, stretching just orientates the form II crystallites without starting any phase transition to form I. Third, as the concentration of 4M1P counits is increased, the phase transition is accomplished with different orientations, which determines the microscopic stress applied to lamellae. Then, detailed kinetics of the II-I phase transition was correlated to the stretching stimuli of the total true stress, component stresses parallel and perpendicular to the c-axis in the crystal lattice. It was interesting to find that transition kinetics is dominated by the component stress perpendicular to the c-axis for the off-axis orientation pathway. For the molecular mechanism of the phase transition, this indicates that the activated chain lateral slip is the dominant process for nucleation of form I within original form II.