Is expiation obligatory upon one who swore to make his sister cry if she did not open the door, and then did so; and upon one whose mother swore that she would not go with her to the farm, and then she went?

If your sister opened the door before or after the specified time, after what you swore upon was depleted, then no expiation is due from you. However, you should not have hurt your sister, and you should have expiated for your oath, based on the Prophet's (peace and blessings be upon him) saying: "Whoever swears an oath and then sees something better than it, let him expiate for his oath and do that which is better."

As for your going with your mother after you swore not to go with her, expiation is incumbent upon you, because what you did was the correct thing. Expiation involves feeding ten needy persons, or clothing them, or freeing a slave. If you are unable to do so, then fast for three days, with a note to condemn excessive swearing, as Allah Almighty says: "And guard your oaths" (Quran 5:89), and the Prophet (peace and blessings be upon him) said: "An oath is either broken or regretted."