lindi, you have drawn a very short straw, but I dont know that SA is the right place for her, unless you are rolling in cash and can afford counselling and she can go on your medical insurance - presumably not, if its a pre-existing condition?
Does she have insurance at least, in case of medical emergency? If not, Id be screaming blue murder down the phone to your rellies. They have really done the dirty with you.
While I think cozy chats are lovely, I do think you need to set some deadlines for things, because if the child is seriously that ill, then she needs specialist help, and unlike the UK, that does not come cheap.
Also, be careful that she is not out of the UK for so long that she is no longer eligible for free healthcare - otherwise, you may find yourself with a very expensive albatross around your necks.
In the short term, did she bring her medications with her? If not, Id get her to the GP ASAP so that she can start treatment as ADs take some time to start working. You also need to have a strategy in place if she refuses to take them.
Finally...you have your own family to take care of and they must come first. Its lovely that you are helping your niece, but she is nearly a grown woman, and you have young children to take care of, so you do need to do what is best for your whole family. That may mean being really tough with her, especially if there is any risk of your children eg seeing her self harming or being around if God forbid, she tries to kill herself.