We study the temperature dependence of the optical conductivity of rare-earth nickelate films of varying composition and strain close to the antiferromagnetic ordering temperature, TN. Two prominent peaks at 0.6 and 1.3 eV, which are characteristic of the insulating phase, display a small but significant increase in intensity when the material passes from para- to antiferromagnetic. This observation indicates the presence of a positive feedback between antiferromagnetic (AF) and bond disproportionation (BD) order. By analyzing the temperature dependence near TN, and using a Landau-type free-energy expression for BD and AF order, we infer that BD order is a necessary condition for the AF phase to appear, and that the antiferromagnetism contributes to stabilization of the bond disproportionation. This model also explains why hysteresis is particularly strong when the transition into the insulating state occurs simultaneously with antiferromagnetic order.