Are you sure they'd cancel the flight because of fog? I've been on a fair number of flights which have either taken off or landed in fog, or other adverse weather conditions such as driving snow, tropical rain, duststorms, etc. I've experienced delays, but never cancellations, and only once been on an aircraft which had to divert for landing, this due to severe crosswinds at Lerwick in the Shetland Islands.
I've never bought two tickets on a 'just in case' basis, and it would have to be something akin to a 'life or death' situation to make me do so.
Hopefully Sue, the extra ticket didn't cost you too much, and will prove worth it.