Getting ready for a power upgrade

So, we are getting ready to upgrade the power set up of our 2003 Allegro Bus from a 2000 watt modified sign wave inverter/charger to a pure sign wave inverter/charger. We will also be adding 300 watt solar with an MPPT charge controller. We've received some great insight from a friend of ours, but looking to see what others might suggest.

Quite frankly, we are not quite sure why they sold this RV with a Modified Sign Wave Inverter. The microwave has never worked right on it. I'm wondering if we should replace the current Inverter/Charger with just an inverter and then leave it up to the 'Solar' to charge the batteries, or if we should indeed do a one-for-one change out. Currently. we live full time in our rig and have it parked at an RV park in Sacramento. The rig is under trees, but the end I plan to put the panels on is pointed south and has a fairly clear exposure to the sky.

If we go with the Inverter/Charger route, is there going to be any problem with there being effectively 'Two chargers' on the battery bank.

Lastly, we currently only have about three outlets on the 'Inverter'. Should we keep the wiring the same and again only energize the three outlets, or should we make the process a little more manual where I plug the RV 50 amp plug into an interior plug, which is powered off the inverter when we unplug from Shore power. If we take that approach, how do we keep the inverter from trying to charge the batteries (Because it is getting 120 volts from it's power source) and draw from them at the same time.

I'd really welcome any and all input. Thanks!