Welcome back to the Disney Parks Moms Panel, Sarah!
First, I have to say, I love your vacation style! Your family hitting up Extra Magic Hours before heading to Epcot® to meet you at the finish line for the Wine & Dine Finish Line Party makes you my kind of people!
I have been told by a runDisney cast member that the Monorail line to Epcot® will be open at that time. However, if it's not, I have an alternative suggestion for you.
From Magic Kingdom; board the Resort Monorail and exit at Disney's Polynesian Village Resort. From there, your family may take Event Transportation to Epcot®. Disney's Polynesian Village Resort is considered a host resort for this event, so there will be busses running all through the evening to take spectators and guests to Epcot® - so your family will be able to get to you with no problem and no taxi fare.
I hope this information is helpful, Sarah! Please let me know if you should have any additional questions as you plan and prepare for a weekend of wining, dining and running during the
2014 Disney Wine & Dine Half Marathon Weekend.
Cheers!
Faith