Hi Michelle,
I'm happy to clarify
monorail use a bit further and thanks for stopping back with your question.
Park tickets are not needed to use the monorail.
Many guests staying off-site or even on-site do not have park admission. Some guests are there for business seminars, others just want to relax by their resort's pool, and some are visiting just for the day to enjoy a meal and shopping. Therefore, there are a good amount of people on WDW property that do not hold a valid park admission ticket to any of the four theme parks at Walt Disney World.
The only exception to this flexibility with WDW transportation can occur during extremely high crowd times such as New Year's Eve!
Everyone in your party regardless of whether they have an admission ticket will be able to use the monorail, boats, and/or buses on WDW property.
I wish your family a fun breakfast at Chef Mickey's!