Yep, the propane grill connection on your TT is low pressure (already regulated) and is made for low pressure grills without a built in regulator.
On some of the Colemans, you can do away with the regulator installed on it. There are multiple youtube videos and several postings on these forums how to do it.
If the regulator is built into the assembly with your on/off knob, as some Colemans are, it can make it a lot more problematic to do what you are trying to do.
I've been involved in several of these previous discussions. Let me search on my history and see if I can locate them for you.
Many members end up putting a tee at the TT propane tanks and then run a line from the tee directly to the Coleman. This way you don't have to do anything to the regulator, as you are getting hi pressure propane directly from the tank, and then your Coleman grill regulator can operate as it should.
Here's one on that:
Another Coleman Roadtrip grill conversion ??