How to move the badge before today text?

If you want to show Open and Closed badges before the today text, you can add these to your custom style:

/* for open badge */
#adv_business_hrs-4 .open-status {
    float: left        !important;
    margin-right: 10px !important;
    margin-left: 0     !important;
    line-height: 1.1   !important;
}

/* for closed badge */
#adv_business_hrs-4 .closed-status {
    float: left        !important;
    margin-right: 10px !important;
    margin-left: 0     !important;
    line-height: 1.1   !important;
}

the number 4 in #advbusinesshrs-4 is the widget ID. This number is unique for every widget. You can find this ID in the shortcode tab.