Wow, potty training is one of those things where there is a HUGE variance in methodology, huh?
I have only worked with my own kids. 2 boys and a girl. Haven't had to do any d/c kids, as they either already were, or have been too young.
My oldest we used sticker charts, and a lot of patience. He was trained around 2, but then we had a baby so he regressed a little. I wasn't too worried, as he was still young. We tried again at 2 1/2 and had no real issues. My second boy was a stubborn one. He refused to even try until he was just about 3. And then, I swear that he just decided he was a big boy. We continued to talk to him very positively about the whole thing, about how big boys wear undies and go on the potty, and 3 year olds don't wear diapers, etc. We used to put Froot Loop cereal in to the toilet and he could "aim" at it. My daughter, admittedly, virtually trained herself, at about 2 and a half. She got undies in her stocking from Santa (not that we thought she would use them right away) and decided over Christmas break that she needed to start using the potty! With all of them, we introduced the concept of the potty between 18 months and 2 years, but didn't expect anything until a little over 2 to 2 1/2.
I am not a huge fan of using treats, I have heard of children who will control their urine and poop so that they can get more candy, etc and that is not a good habit or good for their body. Many people have used them with success, though, so it's a personal preference.
For the dayhome, I ask that children have had a decent amount of potty success at home before we even try it here. Like the posters above mentioned, daycare is so much busier than home, it can be tough to interrupt a kid who is playing to go potty. So they need to understand what is going on, be able to vocalize it, and so on. I don't mind taking a child to the washroom every hour or whatever, but I don't have the ability to hang out in there for more than a few minutes. I don't mind using either undies or pull-ups. Especially at sleep time, since sometimes kids have a hard time with staying dry while sleeping (my own kids were like that, and I still put a pull-up on my 4 year old at night, even though 99.9% of the time it's dry in the morning).
20 months is awfully young to be completely trained, so I am thinking it's a little bit of mom and dad being trained to time it properly. Not that kids can't be trained by then, but if she is freaking out and having all kinds of accidents at your place, I would put the diapers back on and give it some more time, personally.