Vibrational environments are commonly considered to be detrimental to the optical emission properties of solid-state and molecular systems, limiting their performance within quantum information protocols. Given that such environments arise naturally it is important to ask whether they can instead be turned to our advantage. Here we show that vibrational interactions can be harnessed within resonance fluorescence to generate optical states with a higher degree of quadrature squeezing than in isolated atomic systems. Considering the example of a driven quantum dot coupled to phonons, we demonstrate that it is feasible to surpass the maximum level of squeezing theoretically obtainable in an isolated atomic system and indeed come close to saturating the fundamental upper bound on squeezing from a two-level emitter. We analyse the performance of these vibrationally-enhanced squeezed states in a phase estimation protocol, finding that for the same photon flux, they can outperform the single mode squeezed vacuum state.