i guess the dealer didn't tell you about the parasitic power drains RV's have.
you're right about the alarms and also, the radio and a few other things will drain a battery dry in just a few days.
the solutions are to keep the trailer plugged into shore power or like most of us do, installing a battery disconnect switch.
they can cost anywhere from $5 up to $35. the most popular are the ones available at marine supply stores.
do a search here on battery disconnect switch and you find tons of threads on the subject, with pics.
and Zoe the Wonder Dog(R.I.P.)
'07 Roo 23SS pushing an '07 Chevy Avalanche
Equalizer WDH and Prodigy BC