To ground or not to ground: portable power supply
CONSIDER a system with 


Metal case grounded to 12V negative, with 12V positive well isolated from user contact making 12V user contact very low possibility. 
Then float the AC supply. Make it very hard to contact either AC leg. 


In outdoor situations if you get  good contact between user and ground and between one DC battery pole and ground and if user makes body contact with the other DC pole you CAN get strong user-muscle-lockup.
I know of it happening to a friend standing in water (flounder fishing, 12V LED light) - much less likely with your application. 

Locking all 12V+ inside a full metal 12V- "full metal jacket" makes contact "impossible" [tm] - keep it that way !!!. 

Having AC floating allows one lead contact without harm.
The same would be true of the battery BUT AC is much less liable to cause can't let go shock. 

DO NOT common DC and AC  sections for same reasons.