It's nothing Ivo said, it's the circumstances that Vanamonde and the Assistant are presented. And she can't be his sister as Van seems to be an only child at the time of his father's death and his mother did not appear to remarry.

It's my take on the relationship. The presence of some random child in that situation is rather odd, don't you think? She is the child of some one in that room (Occam's Razor).