From the way you're describing your load situation, you might want to consider two 1500or 2000 watt inverters, . . .one on each 120V leg. Then you would have enough AC power to run everything (and future everything as well)
It's not advisable to run 2 roof AC's or other high wattage components on one 120V leg especially when on generator power as only one set of windings will be (trying) to pull everything.
I wouldn't necessarily invest in pure sinewave inverters due to cost vs application. Most 120V RV components are quite happy with a stepped square wave (modified sine), which is what you get with an Xantrex or Trip-lite non-SW.
China made (el-cheapo) inverters IMHO are usually trouble sooner or later, . . .usually sooner.
Most put out a trashy square wave and things like rotory AC compressors don't like that, they tend to run hot(er) & ultimately require more wattage.
Computer power supply's, refridgerator circuit boards, furnace circuit boards, TV's etc,. . .don't like it either, . . .some won't even work.
I would suggest an integrated inverter/3 stage charger as they will automatically go from 120V AC to charge mode, . . .however I would get a separate transfer switch.
RV Surplus & Salvage in Elkhart stocks a good 50 amp 220VAC switch with a 30 second load transfer delay, for around $50. The delay is a good feature when you are going to generator power, as it gives the gen time to stabilize after start-up, before taking on the load.
Check with them on inverters & converters also, . . . ask for Trina (she owns the place)
Also check this website Backwoods Solar Electric Systems
there is some good info there, along with inverters & solar panels for sale. (inverters are probably less than from Trina)
Hope this helps.