I'm currently building an "off-road adventure SCUBA support trailer" (pict attached). I designed it with a removable tongue, specifically to enhance security. While someone may break into it, and while someone may haul it away via one mechanism or another, I think that lack of a tongue (including the electrical hookup, which is also quick-disconnect) is a pretty good deterrent to keep someone from stealing the whole trailer. This can be an issue when you go out camping in the middle of nowhere and leave your rig behind while you go hiking or whatever.
FWIW - the trailer has welded on (quite securely, and well reinforced) two standard receiver hitches (in-line), about 24" apart. The removable tongue slides into both of these and is held in with two standard hitch pins. You could also put in two of those hitch pin lock things into those holes when the tongue is NOT attached, just to make it harder for someone to try to put their own tongue or something else in there to haul it away.
The electrical runs down through the center of the tongue (square tube) and exits one side of it, just after it meets up with the trailer frame - and connects via a 9-pin connector to an electrical socket under the trailer frame. So, no tongue, no electric. And because it is a 9-pin connector, much less chance of someone coming up with something on the spot - it would have to be a well-planned heist.
As an added bonus - removable tongue makes for easier storage in the driveway too - just take that sucker off and lots more space in the driveway
Recommend you do something like this on your replacement trailer, or on the one you have if you get it back.
Sorry about your trailer, but nice to get some validation for my trailer theft paranoia and the extra work it entailed.
Hope you get the bastards - or at least your trailer back.
Cheers!
ND
p.s.: picture shows work in progress - still missing fenders, doors and front side panels. That green is primer - will be painted silver to match the Jeep.