One complicated power discussion is not enough for you ??
Sorry, make that TWO existing threads covering the same information.
I think this has been covered in your other threads:
You wire the solar DIRECTLY to your batteries.
You put a switch on the converter so you can shut it OFF when the solar is active if you must but I don't think that is a good idea as it is just another thing you need to remember to do that really is unnecessary.
The power drawn from the AC source will automatically go down some when the solar is active anyway.....so I think you should NOT worry about this.
It is likely to cause you more trouble than it is worth.