My 2p on this would be that my personal view is that depression isn't a cause of T2, but those with T2 are more likely to be depressed, and those why have been running high for some time, it could be a spin-off of the diabetes. Those who arrive, feeling, tired, lethargic, dehydrated and so on may have at least a margin of their diabetes as a result of just plain old feeling awful for a long time.
On the topic of trying to encourage your sister to be tested, again personally, I would never suggest to anyone that they test because they carry weight. We know that not all overweight people become diabetic, so whilst that might have bumped up her chances of becoming diabetic, she may be perceiving you as gloating and picking on her. If I wanted a family member of mine to be tested, I would be stress the genetic elements of the condition, saying it could highlight whether she's heading in the direction of diabetes, and if that was the case at least she would have the opportunity to head it off before slipping over into a diabetes diagnosis; a situation you didn't have yourself.
She could be terrified of a diagnosis - especially if she has seen any of the recent coverage of the saw Docs and all the gloom and doom.
I do hope the young man can find some help soon.