I'm guessing the "you need a bigger inverter" suggestion means they were using the built in transfer switch in the inverter?
I had the same issue last year when deciding what and how to wire in an inverter. The recommendation I liked most and followed from the folks here was to add a standalone ATS (Automatic Transfer Switch) to the shore power/inverter circuits to keep the charger, inverter, AC power all powered only when necessary without chance of backfeed, double feed, or conversion loop (battery to AC while AC charging battery)
Then I was able to use whatever inverter size I wanted and use it to power EVERY outlet and AC item in the camper- up to my available inverter amps.
Works perfectly!
http://www.rv.net/forum/index.cfm/fuseaction/thread/tid/29545741/gotomsg/29545774.cfm#29545774