Most docs start with a sweat test. As far as I know, it can come up with false negatives, but not false positives. Genetic testing is probably a better choice, but most docs/insurance companies start with the sweat test. Sometimes even genetic testing doesn't pick up 2 mutations though. With my son the first test from Ambry genetics didn't pick up both mutations, so they did a full sequence test and that picked up the other mutation.
Also, about your daughter being big for her age, not all people with CF are pancreatic insufficient. That is what makes them not properly absorb food and therefore they have trouble with weight gain. Some people with CF that aren't pancreatic insufficient have no trouble gaining weight or keeping it on.
Especially because of the family history of CF and the symptoms you described, keep pushing those docs till you get an answer! Even if the sweat test comes back negative, push for the genetic testing. And if that comes back negative push for an extended panel or full sequence gene test. I hope your daughter is doing well and that you get an answer one way or another. Keep us posted!