Hello Justin,
Welcome to planDisney! I love that you're going to try and meet your family to enjoy the magic together at Walt Disney World. And it's terrific that you're thinking through some key planning details ahead of time. Let's get a strategy in place so you can hopefully skip some stand by lines together, and enjoy using
Lightning Lane passes for your favorite attractions!
While there won't be a way for your family to add you to their previously booked Lightening Lane passes, depending on availability there is still a good chance you can align some of your reservations that day. The goal will be to find some Lightning Lane passes for yourself that have a time window which even partially overlaps theirs... then you can all scan in at the same time and ride together. Woo hoo!
If your family won't be with you at the time of your ticket purchase, I recommend finding out their Lightning Lane reservation details ahead of time, so you are prepared. After purchasing your ticket, link it in the My Disney Experience app as soon as possible. Then on the home page under Lightning Lane, go to "Purchase", select the date, park, and whether you want a Lightening Lane Multi Pass or Single Pass (or both). The next steps will display available attractions and return time windows. If you can't match all your family's passes exactly, I recommend trying to select experiences with as early of a return time as possible.
In the case of Multi Pass, even if you can't align all 3 reserved experiences... you will all have another opportunity to make an addition day-of selection once your first experience is redeemed. Doing so at the same time may allow you all to select the same attraction and return time.
I'm not sure which park you plan on visiting, but I thought I'd mention your dates fall during EPCOT's
Festival of the Arts, which you may want to check out. They feature delicious specialty food booths during these festivals, along with other fun things like offer cool "artful" photo ops at this time.
I'll be wishing on a start for your plans to work out, Justin! I certainly hope you get to join your family at Disney World.
Have a wonderful time!
Tami