We present detailed chemical abundances of Fe, Ca and Ba for 17 globular clusters (GCs) in 5 Local Group dwarf galaxies: NGC 205, NGC 6822, WLM, the SMC and LMC. These abundances are part of a larger sample of over 20 individual elements measured in GCs in these galaxies using a new analysis method for high resolution, integrated light spectra. Our analysis also provides age and stellar population constraints. The existence of GCs in dwarf galaxies with a range of ages implies that there were episodes of rapid star formation (SF) throughout the history of these galaxies; the abundance ratios of these clusters suggest that the duration of these burst varied considerably from galaxy to galaxy. We find evolution of Fe, Ca, and Ba with age in the LMC, SMC, and NGC 6822 that is consistent with extended, lower-efficiency SF between bursts, with an increasing contribution of low-metallicity AGB ejecta at late times. Our sample of GCs in NGC 205 and WLM are predominantly old and metal-poor with high [Ca/Fe] ratios, implying that the early history of these galaxies was marked by consistently high SF rates.