Update--so far
We submitted to United, and as expected, they declined to offer any refund. However, I felt I should submit to them so I would have the paperwork for the Visa insurance, saying they declined to reimburse the second flight. So, I then put in a claim to Visa, sending a ton of documentation. They are apparently close to making a decision. On the phone, they had said that they probably would cover the accomodations we missed, and didn't know if the flight would be covered. Anything we get back would be a bonus....