question

I use a 3000 Watt inverter on 3 Battleborn's Mine has a built in transfer switch and is built for 50 amp service.

You mush have a transfer switch in the system so you do not burn things up. This will allow shore power to flow through it and not run the inverter.

Victron's 2000 watt inverter is 1600 continuous so it might not run run your microwave. Best to get 3000 watt which is 2400 continuous and will run a 1800 watt microwave.

You don't connect one leg of 50 amp service directly to inverter. You will need a subpanel or something like AM Solar's SMS https://amsolar.com/rv-inverter-accessories/50-tsfmb1

200 ah of batteries is on the low side but doable.

I have a 2000 watt Multi and 200 AH Battleborns like you are planning but with a 30-amp service. The multi is between shore inlet and the AC distribution. Works extremely well but you do need to manage loads manually when on inverter.

The best solution would of course add a second inverter for the other leg and at least one more battery. Running two 2000 watt inverters on 200 AH @ 12 volt of batteries would be very marginal.

sglad's solution seems like a good one and covers most of the bases if a second inverter and more batteries isn't in the budget.

A manual switch in the L2 input to the AC distribution panel would do much the same thing but you'd need to move the switch when using shore vs inverter power.

Your original plan to put the Multi on one leg of your shore power is certainly less cost but has the drawback of needing to arrange RV loads to be on the "inverter" side of the AC distribution panel.

There are also manually operated manual transfer switches designed for home standby generators that could allow more flexibility, switching up to 12 circuits between the main AC distribution circuit and the inverter (using the transfer switch's generator input).