Hi @Nicole Fisher8! Great question. I look forward to seeing with other may suggest for this help with this experience. To answer your question, the kiosk cannot be set down to a specific Group Event.
Since these are two separate events that are setup for the one group, you may consider adding the time ahead of the event name. It is already in parenthesis, but maybe putting it in the name ahead of the event will provide another chance for someone to check in to the correct event.
In the first image notice that there are two events for the same group, and they share the same name of "Children's Church". In the second image, notice that I've updated the two events to have the time at the beginning of the event name.