First off I am an electrical engineer but not a qualified electrician. Of course, I DIY almost all my own stuff.
Looking at the Amazon add the factory says in "best conditions" the amperage of the AC unit is 13.2 Amp-AC and based on a simple calc the 30A charger is probably about 4 amps. Your total is then a little over 17 amps. Hopefully, you have at least a 20 amp circuit to plug in at the house for shore power.
My RV had a large 30 amp plug which is probably more standard at an RV park. I guess this is why you want to run from a single 30 amp service.
I think the main decision is whether or not you put a 120V service box with breakers into your rig. If you are just plugging in a single appliance using a regular insulated cable no problems. But with 30 amps and the distribution, I think you reasonably would need to do the breaker box.
Once you start trying to run a 30 amp service, it might be wiser to have a breaker on board. Not sure if code would allow you to do this without your own service load protection? This outlines a 30 amp service and shows an AC on a breaker.
RV Electrical Distribution
This is the safe way to do what you want AC and DC distribution and integrated charger.
Progressive Dynamics Mighty Mini AC/DC Panel and Converter/Smart Charger - 45 Amp
For your situation, I would get a 30 amp outlet (that needs to be wired) and have it power the unit above. Anything less than that you are on your own.
Marinco ParkPower 15A, 20A, 30A, and 50A power inputs
PS I have only looked at this for about 15 minutes, but that is my initial reaction. I don't know what is already on board.
In my rig, I used a single plug variant of this for a 12V@10Amp charger. Everything else is split between CAR and HAUS 12V power. In this situation, I'm just basically plugging my charger into the wall although the charger is located in the van. You could do that with two plugs as shown in the link below. You will not find a 30 amp variant of this probably because to meet code and or safety standards you need a breaker box.