The quantum noise limited sensitivity of cavity-enhanced laser-interferometric displacement measurements depends on the photon flux in the interferometer arms integrated over the measuring time, the kind of quantum states used, and the decoherence rate. Here, we complement the injection of externally generated squeezed states with an optimally tuned quantum squeeze operation inside the interferometer's cavity to reduce the impact of decoherence on sensitivity. We analytically derive the new, generalized fundamental sensitivity limit. Furthermore, we report on the experimental test of the new fundamental bound by combining for the first time externally generated squeezed light with an additional internal squeeze operation. We experimentally demonstrate the enhanced sensitivity independent on the detection loss. Our results apply to a broad range of quantum sensors, from table-top to large-scale, such as gravitational-wave detectors.