Ok, I spoke to the company that installed the fence, and I sent them my pictures so they can see how awful it is.
And then I called Home Depot, which is where we started, through their "Home Services" programs for fences. They are investigating the issue, from the amount of time it took for us to get the fence installed, to the quality of the install itself. They're contacting the installation vendor they use first, and then they'll contact me to schedule a visit to our house to see the fence in person.
There is no way that they can tell me this is the kind of quality they allow their name to be associated with. Especially when you find a picture like this on their main "fence" page on their website for their fence installation services...THAT is the fence I thought I was getting. That is the fence I still want. I'm hoping we'll be able to come to an agreement on this.
Thanks for your comments, everyone! I'm so glad I'm not crazy...