João - The woman who hesitated to get into the boat has been described as "the fat lady" and it has always been reported that she was afraid to enter because of fear, not because she wanted to stay with anyone on the ship.
I have never come across any references to Mme Aubart's actions during the voyage or sinking, and haven't seen any indication that she was reluctant to leave Ben Guggenheim.
Several sources have discussed someone variously described as "a French woman" and "a pretty French girl" who fell and hurt herself slightly while trying to board the boat. I had thought this person had been identified and that it wasn't Mme Aubart or her maid, but looking at the list of those in the boat again, I see they were the only two French women on board.