Custom field group not showing up in this module?

Thanks for using this module! You don't mention it but I suppose you are using Vertical Tabs Responsive module to render the Field group's "vertical tab" together with all standard vertical tabs. To accomplish what you need you will have to do some PHP coding.

1) Reorder vertical tabs: You can try to reorder your vertical tab by altering the weight of your field group. If it doesn't work, you will need to do a custom module in order to render your custom vertical tab (check out Examples module which has an example of what you need). Then It will be sortable by this module by just adding it quickly into the hardcoded list of configurable vertical tabs (see function vertical_tabs_config_vertical_tab_list on vertical_tabs_config.module)

2) Have some tabs hidden: Same as above, once you add it to the hardcoded list, your new custom vertical tabs it will be hiddable by using this module

@Marja Kuijsten Do you need more info? I already supposed you were on D7 ;)

Feel free to reopen if needed