The cash price for the tickets is between $160-180 with the cheaper flights at a slightly less convenient time (an hour earlier) so really, I value each flight the same. And since its wife and kids flying, status and points earned or not, is not material for me. That's what makes this question so interesting for me.

Does one spend higher or lower value miles first?

The idea of Chase points being transferable to hotel is a good one. As is my ability to earn 20K United miles or 6K Chase points every month through work travel.