I have no new suggestions for you to try, at the moment, with the hope of making it work as expected. But …
As a last resort, could you send a clip that ends up with pixelation when converted to DVD by Toast. For the sake of privacy, I suggest you create one short new clip without your young ones in it, but with similar conditions as before, as much as possible (movement, light).
Such a clip could be uploaded to a file sharing site for big files, e.g. WeTransfer, which would provide a download link to share with others (e-mail to yourself to receive the link in your inbox, or change the settings to get just the link).
Perhaps I can detect something extraordinary with the file, that prevents a proper conversion to a sharp DVD-Video. I’m inclined to think it is something special about your file, as my clips didn’t get pixelated as yours did: I couldn’t replicate the issue.
Just to be sure, I’ll ask: You filmed with the smartphone, transferred the clips to a Mac, either with Photos or Image Capture, did not alter the clips in any way with any app, only have Toast process the originals to DVD-Video? Correct?