Tyre Pressures

The 12volt inflators are OK for normal car pressures but caravan tyres are usually way above that and the inflator gets hot. You wait a while and gain another couple of pounds, then let it cool off again

Works fine for me and rarely need more than 1 or 2 extra psi anyway. Some pumps are rated higher than others

Excatly ... RTFM 

Like most things, tyre pressures don't matter significantly until you realise that they significantly matter. Then its usually too late.

A few examples:

My last car my much beloved Shogun recommended increased the tyre pressures for towing, but then I could have been towing a 3.5T trailer with 150kg on the ball. 

My current Santa Fe does not need any adjustment but then it is a very big heavy beast and runs on pretty sturdy high load rated tyres anyway.

The point is that the recommended pressures and loads are calculated by smart people who are trying to keep you safe whilst avoiding litigation.

In many cases the weight is not the primary concern, it is the lateral distortion of the tyre when you get a wobble, this can reduce the tyre contact to a tenth of what you need to keep your shiny side up.