I'd get bells on the door she can ring...whining is very hard to teach. But bells...very easy. Before you walk outside, ring the bells. Maybe try to get her to nudge them. Let her out after that. In a little bit, she'll realize that ringing the bells means going outside.
The fact that she's going #2 inside means she's not potty trained and you'll have to basically start her as an 8 week old puppy. Do everything you're doing by giving lots of praise when she does go outside, but you'll still have to work on things. A dog that defecates inside its crate is going to be hard to retrain...basically she has learned to not care that she's laying in her own poop and its not a big deal. Most dogs don't like that so they hold it and make noise to get out. She has been taught otherwise.
I know ... dogs are supposed to hate pooping where they sleep. I am baffled. I can only think that this stems from the conditions she lived in with the "trainer". When I went there to get her, I saw a number of dogs in crates. I wonder if my puppy wasn't left in them frequently, for so long that she couldn't hold it any more and was forced to go in the crate and just live with it. I wouldn't be surprised. But now she's been out of there for 8 months. How do we un-train this bad behavior?
Yes, I can teach her to ring bells when she wants to go outside. She's smart, I'm sure she'll catch on fast. But I'm not sure that this will fix the problem because she's not even trying to get outside to go. She does not whine or even pace around the room -- she just goes. Last night I was half awake and didn't even know it had happened until the smell hit me!