Minnie Vans are available to anyone with the option is activated in the Lyft app in your phone. At this time, it’s only activated at deluxe resorts. If you are not staying at a deluxe, you may be able to stop by and request access. Reports are hit or miss with that being successful. The service is expected to roll-out to all once the fleet is enlarged; I haven’t read any solid date for that.
WDW buses should be able to accommodate your party. During morning opening or evening closing “rush hour” if there is already another a ECV ahead of you, you may need to wait for another bus.
Enjoy your vacation!