There have been a surprisingly large number of people curious to know what will happen with the competing parties. I thank everyone for their advice and input.
However, luckily, it has become a moot situation.
The other family made the extremely generous offer to move their party to the following weekend so that everyone could attend both parties and no one had to choose.
Dave and I had been trying to figure out an alternate date for Nathan's party but things get very cramped here during birthday season. There are birthday events every weekend from now until the second week of June. We actually began mapping everything out back in January-February just to make sure nothing got overlooked and we didn't end up overwhelmed.
I'm very thankful to the other family. It would have been easy to stick to their guns and assume it wasn't their problem. Instead, they chose to be generous.
Sometimes I get cynical about humanity in general. Probably because I watch too many police procedurals and was a devotee of House (Everyone lies). Gestures like this go a long way towards restoring my faith in the community at large. People really can be considerate, even when there's no underhanded reason to be. They're nice simply because it's the right thing to do.