Gosh i really feel for you in this sensitive situation, because that is what it is really isn't it, here you have a young lady with no social skills ,maybe some mental problems and no idea how to deal with it all, i would say it would be over-whelming, i sure would not like to be in your shoes either, i would also imagine she is grieving for the loss of her father too.

I think saying you should kick her out, is heartless, we would not do that to a stray animal here on PT, and i know there is no way you are even thinking that way at this stage,hang on in there if you can.

I think your best bet is to get some professional help , they may beable to give your ideas how to deal with her, getting her evaluated would make sense first though, as then you would know exactly what you are dealing with, i hope things work out and i admire your courage taking her on, thank goodness she has you to turn to, good luck.