Hi Jesse,
Hooray for a first trip to the Walt Disney World Resort! Make sure you grab your First Visit pin from your Walt Disney World Resort or any park store or kiosk!
Your mother-in-law has a few options to recharge her portable oxygen tank. One is at any Guest Relations office which is generally at the front of the park. The other is any of the
Baby Care Centers located in each park. The Baby Care Centers are a great place to take care of the needs of Disney's littlest guests. There are also outlets throughout the park that might work for your mother-in-law as well.
As for attractions a thirteen month can enjoy, you would need to look at the restrictions. As long as there is no safety restrictions, you are free to bring the little one on the attraction. I would review the attractions prior to leaving so you know what to expect.
Finally, for special things to do, there are many options. You can go to a special character meal at the Crystal Palace or 1900 Park Fare. You can enjoy an activity such a fireworks cruise or have your hair done like a princess. The options are up to you!
Wishing you a magical day!
Beth