Hello, Michael!
What a great tour the three of you have lined up at Walt Disney World's Magic Kingdom Park, and you're going to absolutely love the Treehouse Villas!
Disney's The Magic Behind Our Steam Trains Tour starts at 7:30 a.m., and Guests are advised to meet outside Magic Kingdom's turnstiles 15 minutes prior to the start of the tour. Unfortunately, the earliest buses run one hour prior to park open, which, on the earliest Extra Magic Hour mornings will still only be 7 a.m.
I called Disney's Saratoga Springs Resort and Spa, and was told that you can either have the resort call a cab to pick you up, or to hire a shuttle from Mears Transportation.There is a gate to the entrance of The Treehouse Villas, so I was told that you should arrange to be picked up at The Carriage House (where you check in at Saratoga Springs.) There
is a walking trail that connects Guests at Treehouse Villas to Saratoga Springs, but you'll have to allow for extra time to get between the two.
I'd ask at the front desk, or, if arranging your transportation through Mears, if it's at all possible for you to meet your transportation at the gate to Treehouse Villas. I don't know if this is possible, but it can't hurt to ask.
Either way, your ride can either drop you off at Transportation and TIcketing Center or at Disney's Contemporary Hotel. The second location is only a 5-10 minute walk to the gates of Disney's Magic Kingdom, and it will eliminate your having to rely on another form of transportation to get to Magic Kingdom Park (monorail, ferry, etc.)
I hope this helps! The insight you'll gain on the tour will surely make all of your extra effort seem worthwhile! Enjoy the tour; be sure to send additional questions as you think of them! I'd love to help!