I will make a copule of Inverter recommendations if you like
True sine wave: There are two kinds MSW and TSW, There is a long list of things including electric blankets, clocks and all audio, radio and television gear that may not play nice with MSW inverters.. the last item on the list is "Any device needing more power than the inverter can supply"
The list for TSW inverters is: Any device needing more power than the inverter can supply"
That's the whole list.
Inline/stand alone. If you go stand alone install new outlets, red or orange in color, it powers those. Stand alone's ONLY convert battery to 120vac.
INLINE (Recommended for you for other reasons) can pass shore power to the outlets if you got it (Or generator) and when doing this they charge the house batteries, The converters in these are usually very good 3-stage or 3-stage plus a feature converters. Among the very best out there. These replace your existing converter which in an RV that old may well be a single stage battery killer.
How to do in inline inverter line drawing (I'll skip the 12 volt this line)
Main breaker box,-----Inverter----Sub panel with multiple breakers---Loads.
12 volt---Big heavy cable short as possible---Inverter
Mount inverter in a compartment NEAR the batteries, but not the same air space.
How big
About the smallest TSW you will find is 300 watts, that is enough for computer and televisions as a rule, or if you shut down the computer your electric razor.
A bit bigger insures enough for all the above
1,000 can power a SMALL microwave
2,000 A larger Microwave, TV's Computer, and a bunch of other stuff. (A good size).
Batteries,, you need roughly 200 amp hours per kilowatt of inverter, so a pair of GC-2 Golf Car batteries (230 amp hours at the 20 hour rate) is ideal for a KW. will work with a 2KW but two pair... Better.