Answer:
He needs to ask that question in order to gain trust in himself and know that his children trusted him as well. He want's to be more than the "town drunk", at least to his children.
He want's a reassuring relationship with his family to strengthen the bond and so that they all will be there for the rest because they are related. Altough some of his kids have given up on him, he knows Jeannette will believe in him.
On one occasions Rex taught Jeannette how to swim (by literally forcing her to sink or swim). He repeatedly throws her into a sulfur spring in the desert, rescuing her when she sinks only to throw her back in again. One must believe he has good intentios, he wants to do good, to help.