This is a very common issue
Welcome to the forum first off.
Now, to the grill dilemma.
To make a really long story short (use the search in the forum here to find numerous posts on this)
Your Coleman grill is not an RV ready grill. It comes with it's own propane regulator built into the grill. This regulator drops the pressure of the propane coming into your Coleman to 'grill safe levels'. This regulator that is built into your grill allows you to directly plug your coleman grill into traditional propane sources... like those little green propane tanks, and the larger BBQ grill tanks most of us use at home.
The problem is that your camper already has a regulator on it's own propane supply - so the quick disconnect propane connector on your camper is *already regulated* and therefore low pressure to begin with - You cannot hook up another grill with its own built in regulator to that supply line without dropping the pressure of your propane gas too low. Basically you end up with 2 propane regulators on the same propane line and that's a no go.
The solutions are to 1) buy an RV specific grill that is intended to work with a low pressure propane source.
OR -
Modify your existing Coleman grill so that it will work on a low pressure system (like the one your camper is supplying). This involves removing the regulator that came with your grill and installing a Quick Disconnect on that grill which is compatible with the propane hose you will need to buy in order to plug into your camper.
Here's an example of an 'RV ready' grill that requires no modifications to work with your camper.
Flame King
This is the hose you would need to connect that grill, to your camper and for what it's worth, you will need a hose like this anyway if you ever plan on using the propane connector on your camper. The only real question is do you buy a new grill, or modify your existing one to plug into it.
Camco Quick Connect hose
There is a 3rd option. Some people T Off of the main propane tank that is mounted to their camper, creating an unregulated supply right there at the tank - and they run their BBQ grill off of that, no mods required.
It all comes down to how much you care to spend, vs. how handy you guys are with retrofitting your existing grill to your camper.
Me personally, I use an 'RV ready' grill now, and when that stops being viable in a few years, I will modify my Weber Q grill to work with the camper, understanding that this is a permanent modification to the grill and it will in effect be 'married' to the camper for life. I'm cool with that though
This topic does come up a lot so I'm sure you'll get other replies, and probably already have while I was typing this.