A series of copolyesters, poly(butylene adipate-co-butylene itaconate) (PBABI), was synthesized using melt polycondensation from adipic acid (AA), itaconic acid (IA), 1,4-butanediol (1,4-BDO), and ethylenediaminetetraacetic acid (EDTA). 1H-NMR, FT-IR, GPC, DSC, TGA, DMA, XRD, Shore D, and tensile test were used to systematically characterize the structural and composition/physical properties of the copolyesters. It was found that the melting point (Tm) and crystallization temperature (Tc) of the copolyesters were, respectively, between 21.1 to 57.5 °C and −6.7 to 29.5 °C. The glass transition (Tg) and the initial thermal decomposition (Td-5%) temperatures of the PBABI copolyesters were observed to be between −53.6 to −55.8 °C and 313.6 and 342.1 °C at varying ratios of butylene adipate (BA) and butylene itaconate (IA), respectively. The XRD feature peak was identified at the 2θ values of 21.61°, 22.31°, and 23.96° for the crystal lattice of (110), (020), and (021), respectively. Interestingly, Shore D at various IA ratios had high values (between 51.3 to 62), which indicated that the PBABI had soft plastic properties. The Young’s modulus and elongation at break, at different IA concentrations, were measured to be at 0.77–128.65 MPa and 71.04–531.76%, respectively, which could be attributed to a close and compact three-dimensional network structure formed by EDTA as a crosslinking agent. There was a significant bell-shaped trend in a BA/BI ratio of 8/2, at different EDTA concentrations—the ∆Hm increased while the EDTA concentration increased from 0.001 to 0.05 mole% and then decreased at an EDTA ratio of 0.2 mole%. Since the PBABI copolymers have applications in the textile industry, these polymers have been adopted to reinforce 3D air-permeable polyester-based smart textile. This kind of composite not only possesses the advantage of lower weight and breathable properties for textiles, but also offers customizable, strong levels of hardness, after UV curing of the PBABI copolyesters, making its potential in vitro orthopedic support as the “plaster of the future”.