Hi,
Using shore power and solar at the same time to save on electricity cost is fairly unusual.
Solar is mainly for charging the battery bank. For that purpose--with enough solar wattage the 'converter' may be left unplugged. When the battery bank is fully charged it would be possible to have a controller that is capable of diversion loads. For example a 12 volt water heating element could be installed.
Using a hybrid inverter, it would be possible to limit shore power use during peak solar hours by setting the input amperage way down to 3 or 4 amps. I don't think this is a wise idea.
The other issue is economic. If you had 600 watts of solar it would, under perfect solar conditions, generate about 3 kwh of power per day. At 15 cents per kwh all that would be saved is 45 cents a day.
Where solar shines is when it is compared to the cost of running a gas generator. 600 watts of panels, with an adequate battery bank would pretty much eliminate generator use. The one item that would be not possible would be the air conditioner. For that, a much bigger solar farm would be needed. It could be done, but probably a 24 or 48 volt battery bank with a lithium ion battery bank would be best with about 1800 watts of panels.
If you want to run the air conditioner, head for a low cost campground and use their shore power.