If I was the primary care giver for my now deceased dad and my younger sister and her boyfriend moved in and now they want me out, what are my rights?

Assuming the house was owned by your father you would need to know if he had a will. If he had a will and you are given a portion of the house you would have an ownership interest and the right to stay.  If he had no will you and your sibling would share the property and you would still be able to stay, assuming you father did not have living parents or spouse.  You need to private your fathers estate so your rights to the house are clearly defined. Right now your sister has no more right to the house unless your father placed her on the deed before he died.