I am Jewish. My ex-wife is gentile but her grand- mother was Jewish. Sometime during the WW 2 Shoah, under pressure, she must have converted to Catholicism; somewhat a kin to the Marranos of Spain. In fact, she had impeccable Yiddish, often visited my parents when she came to the US from Poland and recited the Sabbath blessings, etc. I taught our daughter Jewish traditions, Sabbath/festival candle blessings, the "v’ysomeh elohim" blessing for daughters & other religeous rituals. Sometime after the divorce my Ex "quietly" imposed her religion on our daughter. To date, my child, barely gives lip service when cajoled by her mother. Would my daughter be considered Jewish or not?
I assume that when you write that your ex-wife was not Jewish although her grandmother was Jewish you mean that her Jewish grandmother was your ex-wife's FATHER'S mother. If she were the mother of your ex-wife's MOTHER, then your ex-wife would be Jewish whatever her religious beliefs or practices. In any case, your daughter's status is identical to that of your ex-wife.