Gomes As it is clearly written on the sheet you have just posted 30 day extension is at the 'discretion of the Immigration Officer.' You only have a definite answer once you apply.
But look at the other advice given already, that to mention your wife and child simply gives the IO an indication you are trying to game the Visa exempt scheme rather than apply for the correct visa.
Tin Kwuk Lo As I read it, CH nationals can only apply at TH embassy in CH, not in other countries, and its quite hard. Don't know if they are doing same with HK.
UK visa rules are now stupidly enforced as the IO try to cling on to the tiny bit of power they have left, as everyone else can see UK Home office is not fit for purpose.