I am about to receive an inheritance which I know was derived by my father from working on shabbos and charging usurious interest rates. Does Halacha allow me to accept the inheritance?
You may use the money from both the interest and what was earned on shabbos. Although the person who collected interest has to return the money and may not use it, his relatives may use it after it was inherited. Regarding the money that was earned through chillul shabbos, there is also no prohibition on the relatives to use the inheritance.
Y:D 161-6, Poskim.