Cable
The cable you're looking for is Type UF, or Underground Feeder cable.
It can be purchased at big orange, and big blue, by the foot. It's available in 6/2, 6/2 with ground, 6/3, and 6/3 with ground, and is rated for direct burial.
Attachment to Service
There is one temporary, and two permanent ways to supply power to a park trailer.
Temporary
Power-Supply Cord
You'll want to use a NEMA 14-50 receptacle, and 4 wire cord with NEMA 14-50 plug to connect the trailer to the service. The trailer's electrical grounding will be through the service plug, so only the distribution panel will have to be grounded.
Permanent
Mast Weatherhead
You can use four continuously insulated, color-coded feeder conductors strung from a mast to a weatherhead as a permanent feeder.
Raceway
A metal raceway, rigid nonmetallic conduit, or liquidtight flexible nonmetallic conduit, from the disconnecting means to a junction box on the underside of the trailer can serve as a pathway to run permanently attached feeders.
NEC
For reference, park trailers are covered in article 552 of the National Electrical Code.
You can use most types of conduit outdoors, though some will require liquidtight fittings. Cost wise, and due to the ease of use, I'd recommend schedule 80 PVC conduit.
schedule 80 PVC conduit http://static.hardwarestore.com/media/product/636554_front500.jpg
As long as you use the proper size conduit and boxes, you can indeed run all the circuits through the same conduit.
If you used 14 AWG THWN conductors (15 ampere circuit), you could jam them into 1/2" schedule 80 PVC conduit. If you want a bit easier pull, you could use 3/4" schedule 80 PVC conduit. If you're using 12 AWG THWN conductors (20 ampere circuit), you'll have to use 3/4" schedule 80 PVC conduit. I figured for 3 conductors per circuit (hot, neutral, ground), so that's 9 total.
If the circuit is GFCI protected, you can install the conduit 12" underground. If it's not, you'll have to go 18" deep. Since you're installing outdoor outlets, you'll have to GFCI protect them anyway. If you use a GFCI breaker, you can provide that protection, and save yourself some digging.
Wherever you go in or out of the ground, you'll want to install an expansion fitting.
Best Answer
These pull boxes are open bottom (most of them) and are meant to have the underground conduits elbowed up into them since they're only 12" deep. Some might have side knockouts but I haven't run across any. The sides aren't intended to have holes knocked out in them. hope this helps. I don't have code backup, only installation backup.