tefilla - The father's or mother's name in the "Ribbono Shel Olam" (Yom Tov)

In the "Ribonno Shel Olam" prayer which we say on Yom Tov prior to taking out the Torah, there seems to be a major difference of opinion between certain siddurim (prayer books). Some have the individual supplicant give his name and his father's (as in siddur Rinat Yisrael) while others ask for the supplicant and his mother (as the ArtScroll) and include the word "amatecha" (Your maidservant) either before or after to reflect that. Usually, we only invoke the mother's name when we ask for refuah (healing).

Is there some argument about the purpose of this Yom Tov prayer (which does not mention health) which would explain the use of the mother's name according to some texts but not others?

------edit 3 years later-------------

The mother's name is also used in a "avdecha X son of MOM amatecha" in the yehi ratzon for entering the sukkah which also seems not to be about healing. Same question.