Has anyone lost weight doing Core Rhythms or Yoga Booty Ballet?

I have about 50 pounds to lose. Are these good for weight loss, or just toning? How often should I do them?

Yoga booty ballet is definitely a workout that will tone you and get you sweating. It is aerobic and will definitely burn calories. I tried yoga booty ballet for a while and yes, it's a workout! I found it fun and very effective. I had to stop because I was having issues with an old injury, but I definitely would have kept it up if I could have.
You should do a good aerobic workout like that 3 or 4 times a week. Make sure you drink plenty of water before, during and after, and if your goal is to lose weight, make sure it's 8 cups minimum a day. it will help flush toxins that you burn as you exercise and as your body loses weight, as well as helping keep you energized (yes, water does that!) and help stave off hunger until the next meal, assuming you are changing your eating habits! If you don't change your eating habits, you will likely have a difficult time losing much weight, though you will lose SOME if you begin this exercise regimen.
Go to http://www.sparkpeople.com (it's completely free) and sign up, and see what you can find out about a healthy diet. It's too much to explain in an answer like this. :)
There are tons I mean TONS of resources there for people trying to lose weight and get healthier, including a forum full of members who are trying to do exactly what you are doing. You can get a lot of questions answered there.
Do give it a try!

Good luck!