Were there ever issues with the port! You should read the many posts here from 2 years ago, getting to the level of threatening lawsuits.
The issue seems to have come about because the port used on the tablet is a square-ish oval shape rather than a traditional trapezoidal shape matching the USB plug. The result being that some users tried inserting the plug upside down (the contours of the port not preventing this), damaging the pins in the port.
There's been quite a bit of debate over why Dell used the problematic port. Some people pointed to the specs set by an industry group, saying that Dell was required by the standards to use this port.
As a result of the port issue, it appeared that many people were damaging their ports and filing warranty claims, which has resulted in the customer service warranty response you've experienced. Fair--but of course, still sad and unfortunate--for those who created the issue themselves due to the unfortunate port choice, but unfair to people like you. And in my experience, the power port is a weak link in any PC, with manufacturers not strengthening it enough--as witnessed by another PC I have with a loose power port, wobbling around in the case.
Personally, I saw the issue immediately with the Dell tablet and avoided it by purchasing a 4" lead which I leave plugged into the port, and then I plug my power cable or accessories into that. One can also find repair services on eBay which will repair or just replace the port using the more traditional trapezoidal port, for a relatively fair price (starting at $30 or so, return shipping included).
Congratulations--and thanks, on behalf of the consumer world--to you and your wife for persevering! I hope it all works out for you!