Hi there!
I injured my ankles in July of last year, and had a trip planned in Feb of this year --- so I definitely had to work on getting back into shape before the trip.
If your Mom has issues with her thyroid, the biggest thing is to get a full panel of tests (testing T3 & T4 levels specifically - a good endocrynologist will know what this means) and if she fell out of the range, she'd need to be on Synthroid or something similar. And yes, it will definitely hinder weight loss.
The biggest thing to never, ever do is take a pill to lose weight. They are horribly expensive and it's just not the answer. Mainly what a pill is going to do is mess up your metabolism, and make it harder to keep any weight lost off. Also - for someone with a thyroid condition, they could really hurt her horomone levels and cause further damage to her endocrin system. I took Phenerimine back in the day - I know what I'm talking about. Sure, I lost a few pounds right off the bat (mostly because I was manically cleaning my house at midnight every night), but as soon as I stopped taking it, I gained back 10 more than I'd lost.
The reality is that weight loss is accomplished with basic math. Our bodies burn a certain number of calories a day - and if we consume more than that number, we gain. A great tool (free) to figure out what your generic calorie burn is thedailyplate.com (livestrong.com). Also, it's a great tool to use to keep track of everything going down the hatch. And I mean EVERYTHING. It's amazing how many calories are in that thing ya grab and eat without thinking (I am SO SO guilty of this!).
As for what to eat - there are lots of ways to go about it. The healthiest is essentially this - if it didn't grow from the ground, or have a mother, don't eat it. I am learning more and more about what goes into even the most seemingly "healthy" processed foods, and our body just doesn't know what to do with all those chemicals... and can't burn off the calories efficiently. The more natural the food is, the better. And white flour isn't natural.
It's silly but - eat more veggies than fruit, but still get 2-3 servings (and watch what is a serving!) of fruit a day.... 5 servings of veggies... a couple servings of lean protein... fiber... all that stuff that ya hear people talking about. The food pyramid from school.
Also - she has to get moving. Anything - but specifically for Disney, the ability to walk forever is critical. Everything counts - parking in the back of the lot, walking to the library (mine is pretty close), all those kinds of things.
For me, I've had to look at it as an overall lifestyle change. I have been at it since September, and have a long way to go (I struggle with the food thing.... but am planning on ditching EVERYTHING processed next week - FOR REAL!!). I walk about 3 miles a day (sometimes more) and try to add in whatever exercise I can (taking the stairs at work, parking in the way back lots, etc).
I am reading the book Mastering Your Metabolism by Jillian Michaels (Biggest Loser) and I can honestly say it has really opened my eyes to where I've been going wrong --- even counting calories.
Most of all, she needs support! So - have fun! Go for walks! Good luck!