This circuit may do at least part of what you want. V1 is the adapter and V2 is the battery.
D1 and D2 prevent current from flowing back to either source. When S1 is closed (before the relay opens), the diodes D1 and D2 feed along the higher of the two sources to the output. When the relay opens, the battery (V2) is disconnected so even if it is higher than the adapter it will not be drained. It does not matter how long the relay takes, since the diodes will allow one or the other source to power the board during the transition.
There's nothing here that would allow the battery to be charged- not enough information, so this is a yet incomplete answer.
simulate this circuit – Schematic created using CircuitLab
Firstly, the feed to the cameras:
I think, to be safe you should use a low drop-out regulator to feed your cameras - this takes care of slight overvoltages. The KA278R12C is a linear voltage regulator with very low drop out: -
Note that even when the input voltage is at 10V, the device is still able to ostensibly produce 10V at its ouput when delivering over an amp (6 ohm load). I suspect this device will be good enough to feed your camera system but I can't absolutely say because you haven't specified current. There are other higher power devices that would fit the bill.
Can I wire a load to my battery if it is connected in parallel with the charger?
If the battery is lead/acid and the charging current is significantly more than what the camera load takes when attached to the above regulator then yes you can. If the battery isn't lead-acid then we need to know which technology it is.
How can I add a solar panel + controller to the previous circuit?
Playing safe, you can use a relay circuit that activates the relay when the AC power is applied to the charger - the relay contact can switch the battery from solar charger to AC charger in a few milli seconds. Playing a little bit unsafe, it's likely that your solar charger will have a diode in its output that protects the battery from discharge when the sun doesn't shine.
This very same component probably can mean that you can connect the AC charger permanently to the battery (and solar charger) BUT, you may need to add a series diode\$^1\$ in the AC charger's output when AC is off and the solar charger is feeding juice to the battery; the AC charger's output circuits may be activated by the solar charger and it's difficult to say what will happen - worst case it might pop the output transistor in the AC charger - best case no problem.
However, the chances are likely that your AC charger (just like your solar charger) will be protected from reverse voltages when power is down (or sun is not shining). You need to check this.
\$^1\$The diode needs to be a low volt drop schottky type capable of taking the charge current (again, you haven't specified max charging current so it's impossible to say but there are plenty rated for 10A and 20A continuous usage).
Best Answer
Three ways:
get a DC power jack with a switch that will disconnect the battery when it is plugged in
connect the DC jack and the battery to the input regulator with a pair of diodes. So long as the DC input voltage is larger than the battery voltage, power will be drawn almost exclusively from the DC input
put a series PMOS transistor in the battery connection and wire it up so that it is turned off when the DC power supply is connected but turned on when it is not. You will need to watch the orientation of the body diode - it may need to be installed backwards for this to work properly. You'll need a diode in series with the DC power supply connection. Then you connect the DC power supply input before the diode to the gate of the PMOS and add a pull-down resistor to ground. When the DC power supply is turned off, the PMOS gate will be pulled to GND and the PMOS will turn on. When the power supply is connected, the PMOS gate will be pulled up to the power rail and the PMOS will turn off.