There sure is a lot of different fittings out there.
A quick google seems to indicate the Dometic two burner has a regulator in it. This gives the first clue - you probably need a hose that can handle cylinder pressure. i.e. a high pressure hose.
The instructions on the Dometic website aren't helpful. They just say connect a hose to the stove and support the regulator while you do it. So helpful.
You could just email them and ask what the fitting is. That worked for me with Primus, sort of, when I wanted to know more about my Primus stove.
Perhaps he simplest thing to do would be to take the whole shebang to a RV/Camping/BBQ store and tell the salesman what you need.
There would almost certainly be a hose available that has the right fitting to connect directly to the cooker.
Then an adaptor for connecting the hose to the coleman bottle. If you get lucky, and I doubt you'd have to be
that lucky - they seem common, you will find a hose that screws to the cooker, and has either a direct connection to the coleman 1lb bottle or can be adapated.
Even here in Outback Oz, adapting a 1lb propane bottle to my 2 burner was not very hard.
I did have the original hose to start with, though.
I was able to buy an off-the-shelf valve assembly that was made to screw on to a 1lb propane bottle (I'm assuming you mean a Coleman green bottle) giving me a valve and a 3/8" BSP LH threaded outlet, at that point the original hose screwed right on.
https://www.ebay.com.au/itm/25432111839 ... gLPtfD_BwE