Hi and Welcome!
Congrats on your Sunny!
Now to your questions, first is a clarification, in your post you mentioned the "220 cord", Heads up!!! That is not a 220 volt AC plug. It somewhat looks like an older 220 volt dryer plug but it is not. That plug is a camper (RV) 120 VAC 30 amp plug. Your camper is not intended to handle 220 volts and will damage it. This is a common mistake and just passing it along so you know.
To your generator question, yes, the easiest and a safe way to do a generator tie in on a camper is by plugging the camper shore power plug into the generator. This prevents any power backfeed to the campground power system does not cost very much. We do it this way ourselves.
Odds are high you will need to buy a 15 amp 120 VAC male to 30 amp 120 VAC female power adapter that will plug into your generator and adapt to the camper shore power cord. You never said how big the generator was. But assuming it fits on the camper trailer tongue, it is a smaller one.
With that adapter you will only be able to pass 15 amps to the camper from the generator, but it will run your fridge. Assuming your generator is large enough to create 15 amps. Basically you are powering up the whole camper. Since this is only a 15 amp setup, you cannot run the roof AC unit if you have one, they need at least a 20 amp supply. Your dorm fridge only runs off of a normal 15 amp 120 VAC outlet.
They make all kinds of power adapters for campers, just make sure you are getting the right prong configuration and voltage for what you need. Here is one brand of the one I mentioned above
If your generator is 3,000 watts or larger and has an actual 30 amp, 120 VAC receptacle on it, then you can plug directly into that and have full power. However I do not think a generator that big will fit on your trailer A frame.
Hope this helps
Current Sunlines: 2004 T310SR, 2004 T1950, 2004 T2475, 2007 T2499, 2004 T317SR
Prior Sunlines: 2004 T2499 - Fern Blue
2005 Ford F350 Lariat, 6.8L V10 W/ 4.10 rear axle, CC, Short Bed, SRW. Reese HP trunnion bar hitch W/ HP DC
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