Full-outs are one of my favorite skills, and totally fun once you get them down.
Learning new stunts can be hard, and depending on where you live, you may be able to take 'stunting' classes, where you learn techniques and work with different bases. This can be an awesome way to learn, the lessons are usually pretty cheap, but I wouldn't recomment it if your cousin isn't used to having her stunt group switched around all the time. Another option, have her take her stunt group to open gym. It's cheap ($5.00-$10.oo), and you can get a lot of practise in and their is usually other groups there or instructors whom can spot and give you tips.
Drills:
Full ups- Using the trampoline or even on the floor, or a balance beam (anything above the ground), have your cousin practise twisting all the way around and keeping her body upright and tight. This gets the flyer used to the movement. Also, you can buy these circular boards (I have no idea what they're called at the moment), which are probably the most AMAZING tool you can ever have...however they can get a little pricey depending on where you buy them. It's a circular device, with a spot for you to put one foot. You rewind it until it clicks and pops into place, and the action will make it spin really quickly in a circle, eventually stopping and allowing you to pull your skill. This is probably one of the best things I have ever used,
Full Up Machine by Core Athletics and Scott "Crasher" Braasch, this is a link to a picture and how it works. It's also great for learning other twisting skills, like full or double downs.
Straight-up extensions- Using a soup can, have your cousin use it to work on her balance, by 'loading' onto it them pulling skills. One-legged extended stunts are really all about finding your core, and keeping everything still and hollow. Personally, I imagine having a rope going through the middle of my body, holding me up like a marianette while focusing on a spot on the wall, all to keep my balance while pulling skills.
I hope I could help, it's kind of hard to explain different techniques, without having visual aid. Goodluck to your cousin, I'm sure she'll get her required skills soon!
Remember to practise, practise, practise! :)
Lily
EDIT: I found this for your cousin,
Tips For Not Falling In One Legged Extension | Fierce Board - We Talk Cheerleading, bye!