So the wine had been open but you put a cork on it and the cleaning lady moved the bottle around with a cork on it.
If the nochri held a closed bottle whether it was either full or partially full, the bottle is permitted. The reason is that this is not the manner of pouring a libation. If the nochri held an open bottle and lifted it but did not swirl the contents around, the wine is still permitted. If the nochri merely touched the open bottle this is certainly permitted.
However, the issur extends even to leaving an unsealed bottle of wine with a nochri.
If your cleaning lady merely touched the bottle or lifted it, it seems as if this would be permitted. If she swirled the contents around, etc., it would be assur. (This is the shita of R’ Yair Hoffman).
The Rosh to Shabbos 17b says that while the wine owned by a Ger Toshav (a Nochri who accepts the seven Mitzvos of Benei Noach in front of Beis Din) cannot be consumed by a Jew, wine owned by a Jew that was merely touched by a Ger Toshav is permitted. This implies that the reasoning why wine touched by a Nochri is forbidden is only because of the concern of Avodah Zarah, and not because of intermingling (for the reason of intermingling should also prohibit drinking wine touched by a Ger Toshav). This is the shitas HaRashah to Avodah Zarah 29b.
It seems that if there is hefsed merubeh, there might be room for leniency, according to the Ramah. Chances are your clesning lady is not a ger toshav, and therefore wine touched by her would not be allowed.