The detailed abundances of 23 chemical elements in nine bright red giant branch stars in the Carina dwarf spheroidal galaxy are presented based on high-resolution spectra gathered at the Very Large Telescope (VLT) and Magellan telescopes. A spherical model atmospheres analysis is applied using standard methods (local thermodynamic equilibrium and plane-parallel radiative transfer) to spectra ranging from 380 to 680 nm. Stellar parameters are found to be consistent between photometric and spectroscopic analyses, both at moderate and high resolution. The stars in this analysis range in metallicity from -2.9 < [Fe/H] <-1.3, and adopting the ages determined by Lemasle et al., we are able to examine the chemical evolution of Carina's old and intermediate-aged populations. One of the main results from this work is the evidence for inhomogeneous mixing in Carina and therefore for a poor statistical sampling of the supernova contributions when forming stars; a large dispersion in [Mg/Fe] indicates poor mixing in the old population, an offset in the [α/Fe] ratios between the old and intermediate-aged populations (when examined with previously published results) suggests that the second star formation event occurred in α-enriched gas, and one star, Car-612, seems to have formed in a pocket enhanced in SN Ia/II products. This latter star provides the first direct link between the formation of stars with enhanced SN Ia/II ratios in dwarf galaxies to those found in the outer Galactic halo (Ivans et al.). Another important result is the potential evidence for SN II driven winds. We show that the very metal-poor stars in Carina have not been enhanced in asymptotic giant branch or SN Ia products, and therefore their very low ratios of [Sr/Ba] suggests the loss of contributions from the early SNe II. Low ratios of [Na/Fe], [Mn/Fe], and [Cr/Fe] in two of these stars support this scenario, with additional evidence from the low [Zn/Fe] upper limit for one star. It is interesting that the chemistry of the metal-poor stars in Carina is not similar to those in the Galaxy, most of the other dwarf spheroidal galaxies, or the ultra faint dwarfs, and suggests that Carina may be at the critical mass where some chemical enrichments are lost through SN II driven winds. This project is partially based on VLT FLAMES spectroscopic observations obtained at the European Southern Observatory, proposals 074.B-0415 and 076.B-0146, and partially based on MIKE spectra gathered at the 6.5 m Magellan Telescopes, in Chile.