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.

Your appliance is really three hob-pairs, each of which runs off of 230VAC 50/60Hz 1 phase, pulling 16A. This means that your proposed wiring scheme will work out from an electrical standpoint, which is the good news.

The bad news, though, is that for most cord types, carrying 48A requires the flexible cord to have 6AWG conductors as per Table 400.5(A)(1) in the NEC. Considering it looks as if the terminals on your stove will accept neither 6AWG conductors nor spade- or ring-type terminals (most range cords terminate in the latter to fit the terminal blocks on US electric ranges), finding a cord that you can use for this is quite hard -- in fact, no premade cords for this job exist! This leaves you with two options -- make a custom cord that terminates in a standard NEMA 6-50P and use jumpers in the appliance's terminal box to configure it for single phase operation, or use a customized power cord to route the 3 individual hots back to the plug and jumper all three hots together in the receptacle's junction box. I'd recommend the latter as the parts for it are going to be much easier to find -- 10-3 W or G cords generally don't turn up! (Certainly, the orange and blue borgs don't have 'em, nor do your typical industrial suppliers...) Of course, you can always see if your hob will accept a hardware-store range cord -- you will need to jumper in the wirebox as your electrician suggests, and leave the cord's neutral unconnected (cutting off the spade terminal, if present, and using heat-shrink or a wirenut to insulate it would be wise in this case).

Using a three-phase cord and receptacle

You will need a NEMA L22-20P plug and a NEMA L22-20R receptacle, as well as some 10AWG THHN for jumpering in the stove outlet junction box, and the correct wire nuts for connecting the existing 8AWG branch circuit wires to the 10AWG jumpers.

First, cut the existing plug off the cord and wire the L22-20P in its place (if the existing cord cannot be reused for some reason, you will need a length of 10/5 flexible cord to replace it with)). You will need to jumper the appliance for a Y (Wye) power configuration.

Then, take each HOT terminal on the receptacle and wire a 10AWG pigtail to it. Twist all the HOT pigtails together and wirenut them with one of the special wirenuts to the black wire on the branch circuit. Then connect the red wire on the branch circuit to the receptacle neutral and the bare wire on the branch circuit to the receptacle ground. Finally, cap the white wire from the branch circuit off with a wirenut before installing the receptacle.

Making your own cord for a 6-50 plug/receptacle

Making your own cord for this application will require a length of 10/3, 75°C type W flexible cord (a 10/3 type SC or type G cord can be substituted, as these types use the table 400.5(A)(2) ampacities instead of table 400.5(A)(1)) and a NEMA 6-50P plug. You will need to install a NEMA 6-50R receptacle as well -- neither the NEMA 10-50 nor the NEMA 14-50 is apropos for this application, although the latter can be used in in conjunction with a NEMA 14-50P to NEMA 6-50R adapter rated for 50A.