You apparently don't comprehend the intentional ridiculousness of the whole scenario of the commercial, so no, I guess you wouldn't be able to explain it to your kids. It was supposed to be humor, but you saw man-lips touching and lost all ability to see beyond that.
Let's pretend instead that the commercial had featured a woman in a NY deli worker's uniform talking with the heavy-duty Brooklyn accent as she handed out lunches prepared with Heinz NY Deli Style Mayo to her proper British family. Does this help you see what the ad people were after?
OK... I've pretended, but fill me in so that I can pretend consistently...do the kids call her dad? Does another woman rush out and do they kiss on the lips and does the "dad" say see you soon "sweet boobs"?