OP may have handled this all wrong. If he had insurance to cover this mess, all he needed to do is to book whatever he needed and then sort it out afterwards, knowing that he would be covered. No need to argue with UA agent at IAH, no need to spend time on hold with UA getting rebooked to CUN and so on. No need to worry about refund of non-refundable hotel.

If OP didn't have coverage, this is a good example of why you need coverage. It's generally cheap and there is no compensation for delays outside the carrier's control such as weather. Small properties tend to be, for good reason, much less forgiving when it comes to weather-related cancellations. They just can't afford it.

At this point, I would focus on the insurance. The rest doesn't matter if there's coverage.