What an awful thread. So many ignorant comments about PND, it's painful to read.
op, you seem to presume a lot about the inner workings of your sisters mind, her intentions and motives. How exactly do you know she is "using PND as an excuse to avoid family", "embarrassed by family", "looks down on you" etc? These are all your speculations, unless you're going to tell us she has admitted thinking these things?
PND causes you to act irrationally, it can make you very defensive and oversensitive. She needs her family to be supportive, and from the way you talk about her here I bet she can sense your judgement and resentment a mile off. I can completely understand why she would want to keep her distance.
I'm sorry about your father, what an awful situation. However sad though, your sister still has PND and nothing can "snap her out of it". As I said it makes you think irrationally, and at times selfishly. All you can do is focus on how you can get through the next few minutes, the next hour, the next day, and hold it together the best you can for your kids. You become blinkered. It would be great if she could say "now dad has had this diagnosis I'd better snap out of this PND so we can enjoy the time we have left" but this is simply not how it works.
I'd also suggest you stop judging her for trying to socialise and having beauty appointments etc. Have you considered she is doing these things to try and combat the depression? Or should she be at home moping around all day if she was "genuinely" depressed.
Seriously, the comments you have made about her "using PND as an excuse when it is convenient" is ignorant and sickening.
These attitudes are why there is such a stigma around MH. So sad.