OK, I see that your company has a requirement over and above the regulatory requirements. That's fine (but things would have been sped up if you'd indicated it was a company thing, not a regulation), but I can assure you it is not the case with "most' airlines, at least not those operating under JAR.
I've worked for a total of 5 Airlines. An Australian major, a Japanese operator, A European Charter company, A European Lo-Co and now a large ME based international which complies with JAR.
None of them, nor, as far as I am aware, the likes of BA, Lufthansa, VA etc have any requirements over and above the regulations.
The OP asked what the weather requirements were for non-ETOPS en-route alternates. From a regulatory standpoint, and for the actual operation of most airlines, there ARE none, planning or otherwise.