Hi Stephen,
Thank you so much for visiting the Disney Parks Moms Panel with your question. It sounds like you have a great vacation planned!
Disney's Saratoga Springs Resort & Spa is a lovely and relaxing resort. One of my family's favorite things to do is to explore the various dining options at Walt Disney World. There are so many fantastic restaurants! Heading to different Walt Disney World resorts is a fabulous way to explore the variety of dining options.
You will be able to park free of charge for your dining reservations. If you are traveling to another resort, simply let the cast member at the security booth know that you have a dining reservation at that resort, and they will direct you where to park. Since you are staying at a Walt Disney World resort, you will also be able to park for free at the Disney theme parks, which will cover you the night that you are at Epcot.
Please do note, though: you mentioned that on the evening that you are dining at Epcot, you are not visiting Epcot that day. You will need valid theme park admission to enter Epcot, even if you are only dining there. If you have an Annual Pass, or if you are visiting another theme park that day and have the Park Hopper Option on your ticket, that will work to gain entry into Epcot. Otherwise, you will need to have a valid day of theme park admission on your ticket to enter Epcot for your dinner.
I hope that this information is helpful for you, Stephen! Have a great time planning your vacation, and please do not hesitate to ask if you have any further questions.