Plug your umbilical cord into your truck, with the engine running. Should give you enough power to run one at a time without damaging anything. I've done this with a dead battery to operate my jacks. When we had a 27ft. TT, this was a common thing until I learned to disconnect the battery in storage.
If your trailer is going to sit idle and not plugged into shore power for extended periods, it's highly recommended you either install a battery cut-off switch or disconnect the cables at the battery. There are devices inside the trailer that have a parasitic current draw, such as the LP detector and any digital clocks/radios that are part of the trailer.