Hi Shannon! You've got your hands full, but I can't think of any other place that will dazzle your children like Walt Disney World Resort! And nothing is easier than using the monorail to get to and from Magic Kingdom.
Disney's Grand Floridian Resort & Spa is a beautiful place to stay and defined by one word...exquisite! And of course it's a monorail resort so you'll be able to roll your stroller right on without having to collapse it. The walk from an outer building room to the monorail and bus/boat transportation stops isn't too not to far, you'll get there in less than 10 minutes.
One thing I loved at Bay Lake Tower at Disney's Contemporary Resort is the ability to walk to and from Magic Kingdom Park. The transportation will either be by monorail or water shuttle to the Magic Kingdom Park. I'd say both are equal in regards to distance to the monorail.
Your children will love the Alice In Wonderland-themed kids’ water play area at Disney's Grand Floridian Resort & Spa....it's the perfect mix of “tea party” and “pool party.” An upturned Mad Hatter’s hat dumps water when it fills up, and an oversized teapot spills water into a series of teacups, showering the little ones below. On the ground, your kids will love playing under sprinklers and waterspouts, or sliding down one of the two mini water slides.
I hope your Disney vacation is magical and memorable!
~Juliette