Let the solar panels charge the batteries while driving. If you need to charge the batteries more then use a generator or a set of jumper cables from the tow vehicle after you've parked.
I agree with others 2x6V isn't enough. For one of our trailers I carried a 2nd set of 6V in the truck along with +/- jumper wires for the first summer. In the fall I slid the propane tanks forward so a larger battery box would go in.
Brakes needs to be on their own circuit. Connected directly to the batteries is best. Never through a battery disconnect. Some people like to fuse the brake circuit others don't. Either way brakes should be tested on a regular basis with 2 methods. One using the brake controller and doing a tug test. The 2nd is to pull the breakaway switch and doing a tug test. Surprising how many people find out they've been hooking up a breakaway switch that doesn't work.
This is the breakaway switch I use. Also carry a spare pin.
Breakaway Switch, Metal
www.tekonsha.com
You may have a 60A converter but all you get out of it s is 30A due to the mini breaker. Under heavy use the mini breaker will be cooked. If the wire is 6ga wire it may be possible to upgrade the breaker but don't use another mini breaker. I've seen many that have failed.
If the converter is a WAFCO it is a pcs of junk. It's a power supply not a battery charger. When on shore power it is best to disconnect the batteries or the WAFCO will ruin the batteries
The wire from the main breaker/disconnect to the batteries needs to be size for combined input of the converter and the solar controller.