Hi Leah! September is a great month for a first visit to Walt Disney World! The parks are generally very uncrowded then, so you'll be able to see and do lots without long waits in lines.
You don't mention whether you'll have park admission for the first night of your trip. Since you're arriving late in the day, I'm going to assume you're planning to start touring the parks the next morning and would like to dine at a restaurant that doesn't require park admission on your first night.
Since your in-laws are staying at the Swan, the restaurants in the adjacent Beach Club hotel would be convenient. If you want a casual meal, consider
Beaches & Cream, which serves burgers and yummy ice cream sundaes. If your family likes seafood, consider the
Cape May Cafe, a seafood buffet where both of your little ones could dine for free.
If your toddler is anxious to see the characters, consider
Chef Mickey's in the Contemporary Hotel. Your little ones also eat free at this buffet and Mickey and friends will stop by the table. After dinner, you can take a ride on the monorail loop -- my kids always enjoyed doing that when they were little!
Finally, Downtown Disney has lots of great options for dinner and is a fun first-day destination. My family enjoys the food at the
Wolfgang Puck Cafe. After dinner you can stroll through the fun Downtown Disney shops.
Have a magical first visit to Walt Disney World! Come see me again at the Moms Panel if you have more questions! I'd love to help!