All of this could have beem avoided if you had applied much earlier for a new passport. Personally I have always renewed a year earlier than the expiry date. In your son's case maybe obtain a temporary passport to get over the immediate problem.
I have always applied for a new UK passport a year in advance of the expiry of a current UK passport. A shame to lose a year but it avoids a lot of these issues.
I had three good friends here, an Aussie, an American, and a Thai, all now dead. Never wanted a 'social life'. These days my Thai family provide all the company I need.
If it is possible to find somebody you can trust to take care of your wife I would recommend you apply personally, with all relevant documents. You should be in and out within an hour. If that's not possible you will need the assistance of an agent. Best of luck to you and to your wife.