I didn't find Mary living with any of her other children, but, I don't know who Charles or Ann Cavanaugh married, if they did, nor where they were in 1891, nor if they were even alive. And, as I said, I didn't find Thomas T. on the 1892 NY census, although he was in NY by 1891.
Andrew B. Kavanaugh on the 1892 Census for Manheim, Herkimer NY, but Mary was not living with them:
https://familysearch.org/ark:/61903/1:1:X36P-RS2Martin Kavanaugh was in Escott, Leeds Co., on the 1891 census and Mary was not living with him.
Bridget Mcnamee was living in Lansdowne Front Tp., Leeds Co., in 1891, and Mary was not living with her.
James & Julia were living in Leeds Front Tp., Leeds Co., in 1891, but Mary was not living with them.
John Gerald Kavanaugh & his family were living in Leeds Front Tp., Leeds Co., in 1891, but Mary was not living with them.