Had a similar problem to what you described but in a motorhome where the slideout motor would run the house battery down before the room was fully extended. Battery would be fully charged according to meter but not enough amps to extend the room. The quick solution was a 600amp jump pack. The long term solution was new larger battery with more amps.
Since yours is a trailer not a motorhome, the charge line from the truck could be undersized. If it was large enough, running the truck engine about 1000rpm should give a boost to the battery to get the job done.
jh
