Welcome to HCM Forum,
After going through your problem I can understand how stressed you might be feeling.
Its important to know that whatever allegation by your sister on you is because of her altered perception regarding you due to underlying illness.Paranoid schizophrenia
is illness where always threat perception present even with close relatives also and this is present even with you - and if she is perceiving threat from you due to illness u can understand why she is reacting like in this way.
Here there is no problem in you ...So Don't feel guilty that u not able to be strong. Though u behave in very soft -good mannered still threat can perceived by her due to illness.So here being to be strong yourself means giving her appropriate treatment by any means either voluntarily or involuntarily - that will definitely improves her complaints regarding you and decrease her crying spells.Your role here as caregiver is make sure that she should attend to psychiatrist
regularly and administering advised treatment regularly to her.
So take psychiatrist opinion earliest and start appropriate management.
Hope this helps.