The cheap trickle charger puts out 950/1000 amp, or 0.95 amp. The fridge draws 2.7 amps. Your batteries will discharge 1.75 amps whenever the fridge runs with the charger on. That does not take into account the lighting. Your batteries will go down.
If you drive a lot and charge from the alternator, the trickle charger may delay the battery discharge by about 1/3. But it is not a good situation for sitting in one place long-term.
On the other hand, you probably do not need a 45-amp converter. Add 3 amps for the fridge, and 2 amps for each 12-volt bulb (less amps for LEDs). If you had 4 "turn signal" bulbs, that would be about 11 amps at night. You could get away with less if the charger was on 24/7 and the lights were on 4 hours or so, running off both the battery and charger.
Here is a 12-amp Chinese converter for $110: http://puxtradingpost.com/shop/produ...cat=280&page=1
The USA manufacturer put these into our camping trailer as original equipment, and it works. I measured the built-in tri-stage charger's performance, and it is spot-on for wet cells. There are no jumpers, switches or pots to re-calibrate it for gel cells, the settings are in software and cannot be reset. It could possibly overcharge a gel cell and cause it to vent, permanently reducing capacity, but it works famously with Marine deep-cycle batteries. Just remember to check the water level once or twice a year.
It also includes space for a couple of 120-vole AC breakers, and includes space for 4 fused DC circuits.
I don't know your opinion of "made in China." And the charging unit is not repairable, if it fails throw it away and get another (but do you really want to pay $80/hour for someone to troubleshoot a $110 unit?). All I am saying is that it is a low-cost option that works for us.
If you really want cheapo-cheapo, find a regulated
power supply that is designed to power a CB radio or other 12-volt device. You might be able to find one at a garage sale.Open it up, and try to find a voltage-adjustment pot. Using a digital meter, set the output down from 13.8 volts to 12.5 volts for wet cells and 12.25 volts for gel cells. This "float charge" will prevent overcharging and boiling the acid. The wet cells will need occasional "equalization" charges, but if the alternator is connected to charge the batteries, and you drive th bus once per month, that should be taken care of. You will also have to watch if the power supply tries to put out more than its rating when the batteries are down. Some units have current limiters, others will start to overheat.
EDIT: Brain Phart! Set the voltage for 13.5 for wet cells, and 13.25 for gel cells. I know what I meant but didn't type it!