Whether volatile ice lines can produce dust rings in protoplanetary disks remains debated. Previous modelling and observational studies place ice lines using smooth, monotonic disk temperature profiles. However, in substructured disks, the midplane temperature need not be smooth: a deep, planetary gap can locally heat, shift and multiply the ice-line locations. We adopt the non-smooth temperature profile of a hot planetary gap and use dust-evolution simulations to study how CO₂ ice lines, which imprint radial jumps in the fragmentation velocity V_(rm frag), affect dust evolution over 10 Myr and the observational signatures. For comparison, we also run models with uniform low (V_(rm frag)=1 m/s) and high (V_(rm frag)=10 m/s) fragmentation velocities. In the varying-V_(rm frag) model, dust piles up with enhanced grain sizes at the two CO₂ ice lines along the gap edges, appearing as clear double rings in dust observations at 13 μm that persist over 10 Myr; at 1.3 mm, it shows only a modest ring-to-gap contrast of a factor of a few, consistent with the shallow, low-contrast rings in ALMA surveys. The uniform V_(rm frag)=10 m/s model instead forms a single high-contrast ring at the pressure bump and suppresses the inward pebble flux to the inner disk by up to two orders of magnitude, whereas the uniform V_(rm frag)=1 m/s model produces only weak substructure and strong outer-disk depletion. We propose a multi-wavelength test to distinguish these scenarios: ice-line rings stay at fixed radii from scattered light to the millimetre observation, whereas a pressure-bump trap produces a single dominant ring whose peak shifts inward at shorter wavelengths.