From what I can tell Debra, it sounds like you want to be able to run your microwave oven, and all your other A/C appliances (sans air conditioner) off an inverter, and to accomplish that, you're considering installing a 2000 watt inverter. An inverter that size will power a microwave oven, but it's going to struggle with only two batteries - even good quality batteries. A lot of it will depend on the size of your microwave, and how the inverter is installed.
Small microwaves use between 500 and 800 watts while heating. Larger size microwaves use 850 to 1800 watts, and modern average size microwaves use around 1200 watts. We've got a large convection microwave oven and eight 12 volt AGM house-batteries, but even so, when the microwave kicks on, the house lights dim for a moment - and that's with a 2800 watt inverter.
If you opt for a 2000 watt inverter, it should be installed as close to the battery-bank as possible, and run thick gauge wire between the batteries and inverter. Don't worry about equalizing your AGMs. Unless there's an indication that they're not holding a charge, AGMs don't require equalization. The best things you can do to keep your batteries healthy is to avoid repeated deep discharges, and fully recharge them as soon as possible after discharging them.
And remember, unless your solar setup has been installed in a non-standard way, none of your appliances actually run off solar power - including the inverter. They run off battery power. Your solar setup is simply an alternative method of recharging your batteries. The power going into the batteries from your solar panels will slow the battery's discharge rate when power is being consumed, but how much so will depend on the load and the charge rate.
Kev