Another option is modify your fridge to run 12VDC or get one that's already 12V. It would probably be cheaper. convert your lights to 12VDC, and your chargers can probably already run 12VDC. Then all you need is a 80$ battery charger from Walmart; no transfer switch, no inverter, etc. If you really must have the blowdryer, or 120V for for anything else, you could get one of these for 129$.
I declined to answer about your wiring diagram because I don't want to steer you wrong. It will depend on what transfer switch you get (if you get one) and which inverter/charger you get. And if there is info available on the internet for the devices you choose. It would be easy for me to draw a block diagram for you now, but it would be just as easy for it to be wrong and end up getting you hurt. Why don't you post links to the devices you have in mind, and we can go from there?
(that is, if you don't decide to go 12V)
I declined to answer about your wiring diagram because I don't want to steer you wrong. It will depend on what transfer switch you get (if you get one) and which inverter/charger you get. And if there is info available on the internet for the devices you choose. It would be easy for me to draw a block diagram for you now, but it would be just as easy for it to be wrong and end up getting you hurt. Why don't you post links to the devices you have in mind, and we can go from there?
(that is, if you don't decide to go 12V)