Ok to do this you will need
1 Converter:May I suggest a Progressive Dynamics 9200 series.. With a Prosine 2.0 you likely have 2 pair of GC2.. So you can get the big one (9280) if you like.
And a junction/breaker box with a SINGLE 20 amp breaker.
UNPLUG from shore power.
Open the Prosine's connections panel 120 volt) remove wires,, LABEL "AC-IN" and "AC-OUT" using a sharpie please (just in case)
Disconnect 12 volt leads (negative all of them) from the battery
Disconnect 12 volt leads from Prosine (Set prosine aside)
Connect 12 volt leads to 9200
Install 9200
Connect AC leads as follows
Ann Neutral (White Wires are connected to the neutral bus
Likewise all GREEN/Bare wires to the ground bus
AC-in and AC-out black leads connect to the HOT supply side bus
PD-9200 black lead to the 20 amp breaker.
Job done.
You might label the breaker and give some indication that you removed the prosine so that anyone who wants to replace it later can do so.
As for your AA battery charger... I have one (panasonic brand) that works with AA or AAA runs off a USB port
You can install 12 volt powered USB ports (Several threads on it) so you need no 120 vac power for that.. in fact mine is pluggded into 12 volt powred USB charge adapter as I type.
They also make 12 volt chargrs (I have or had one)
Here is an example
Home was where I park it. but alas the.
2005 Damon Intruder 377 Alas declared a total loss
after a semi "nicked" it. Still have the radios
Kenwood TS-2000, ICOM ID-5100, ID-51A+2, ID-880 REF030C most times