ggplot jitter geom_errorbar?

You can use position_dodge to achieve both the desired order and the error bars being drawn at the location of the points

ggplot(data = df1, aes(x, y, color = Group)) +
    geom_point(size = 4, position=position_dodge(width=0.5)) +
    geom_errorbar(
        aes(ymin = lb, ymax = ub),
        width = 0.1,
        linetype = "dotted",
        position=position_dodge(width=0.5)) +
    geom_hline(aes(yintercept = 0), linetype = "dashed") + 
    theme_bw()

If you want jitter, I do like this:

ggplot(data = df1, aes(x, y, color = Group)) +
    geom_pointrange(aes(ymin = lb, ymax = ub), 
                    position=position_jitter(width=0.5), 
                    linetype='dotted') +
    theme_bw()