Thanks everyone, it's done
I could cry right now - something so simple has caused me so much of a headache, and I don't even know why!
It turned out after a lot of trial and error, that EXIFTool hadn't actually changed the metadata, it just made Windows display the altered date. I have no idea how, and didn't even know that was possible. Once I figured that out though, I loaded the files from my camera into Lightroom and using amoringello's tip, corrected the Capture Date. It took me a few goes though, as I didn't realise that I had to tell Lightroom to save the changes to the metadata. Once I'd figured that out, I did the same for the photos from my wife's camera. All good, ready to rename.
Except they were even further out than before. The photos from her camera were somehow out by over 12 minutes, a bigger discrepancy than both cameras put together, even though I had a photo of a clock showing the correct time to the second.
Finally everything was looking good. As I was about to apply the corrected time to her photos, Windows decided that a program using 2GB out of 16GB RAM was not good enough, and crashed, so I restarted the computer and started from scratch with her photos to avoid confusion. I tried to load Bridge, as I knew that copying the files to an SD card would let it put the relevant jpg and raw files together, and is what I'm used to, but now none of my other Adobe programs would launch, something had been corrupted.
I had to reinstall the lot, so I stopped for leftover pizza and caught up with Modern Family, then came back feeling a bit calmer. I copied the files to an SD card and launched Bridge. I changed to settings similar to what emalvick suggested, Cake Smash HHMMSSxxx.dng and let Bridge get them from the card. When it was all done, I opened the folder, and there they were. Except the end of the list wasn't where it should have been...
I'd managed to leave one of the failed efforts in the folder, so I had double the number of files. Luckily enough it was easy to fix though, because if it hadn't been, or I hadn't noticed, I think my computer would be lying in the street by now!
I'm going to bed now, and not touching anything related to photography for at least six hours
Thanks again for the help and suggestions