Are the forty liters of oil that the mother received in exchange for harvesting olives counted as part of the zakat-eligible amount due on the 195 liters of oil harvested from the trees of the house?

There is no zakat (definition) on your mother regarding the oil she received in exchange for her service in harvesting her relatives' crops, because there is no zakat on what a hired laborer receives as wages for his work. The zakat threshold for olive oil is five wasqs of olives (grains), not of the oil itself. If the olive grains from which the oil was extracted are less than five wasqs, then there is no zakat on it. If it reaches the threshold, the zakat is to be given from the olives or from the oil, and it is preferable to give it from the oil itself. It should not be given from its monetary value except according to the Hanafis.