In the past I have used diode isolators with two batteries for a stereos. These work well for doing what you want to do.
For switching from one battery to the other.....
You could switch the cables from one terminal on the isolator to the other for the times when you want use the AV battery for starting. However, I wouldn't suggest this to often. The terminals on the isolators aren't real rugged.
Another way to achieve what you want to do is to connect a relay isolator between the two outside terminals on the diode isolator and put a switch on the switching terminal (small terminal). This switch would normally be open and only activated when you needed to use the AV battery for starting the car. Then deactivated once the car is started.
Here is a link that has some good info on both diode isolators and relay isolators.
https://www.youtube.com/watch?v=CGD8HAeg5UA