It would help to know the type of antenna system fitted on your van and its age. If it is a Status 570 or something like that with a VP-range amplifier then it is already DAB compatible. A bit of digging and Googling will reveal all.
If it is the VP-type then three things:
If it has a radio output and a couple or three TV outputs you might ask what is the difference? The TV outputs and the radio output all carry the same VHF/FM, DAB, and TV signals except that the TV outputs are amplified but the radio output is not. Just move the radio cable from the radio outlet to a TV outlet.
DAB signals are ALL vertically polarised, that is the aerial needs to be vertical which may or may not comply with the needs of your TV signal!
DAB is not necessarily transmitted from the same site(s) as your TV or FM signals but as it uses the pull-out rods at the back of the aerial unit (in practice no need to extend them), if vertical it will be omni-directional. If the aerial is horizontal for TV then you may suffer twice, once because the aerial is the wrong polarity and second because when horizontal it is directional then it may not be pointing the right way.
The best way to split the incoming signal to the radio for the two sockets is to use a splitter like
this. You can use the existing cable from the amp to feed the car radio from one of the splitter outlets. You will need to make a F-type male to F-type male cable to link the amp output to the splitter input. Finally I suggest you get a short flexible cable
something like this. If you make the DAB pigtail as caravan makers do with thick cable, the cable will likely push against the caravan wall behind the radio and force the SMB (smaller) connector off the radio.
Finally, consider getting a JVC radio as it has the advantage that many others don't of not forgetting radio memory contents when you switch the caravan power off.
PM me if you need more help.