I also agree with long PDI. I spent one night in the coach before the PDI with the above checklist verifying everything I could, then went through with the tech. By the time the PDI was done, I had a list of about 50 items that needed attention.
I spent 3 days at the dealer (in a full hookup site) before my family joined me for the trip back home. This gave the dealer enough time to properly fix everything that I had found, plus document the stuff that could not be fixed right away so could be fixed under warranty by a dealer closer to home (we bought the coach new so it had the mfr warranty).
As you mentioned you'll want to use all the systems of the RV. You can pretend to be boondocking or dry camping by disconnecting all your hookups and working the generator, fresh water tank and pump, inverter (if equipped), etc. Needless to say, make sure they show you how to dump your holding tanks, too. Sometimes the valves are not in very obvious places.
Make sure the house batteries hold up under load (easy to do if you have a big inverter, just boil water in the microwave for a while). You may want to use a hydrometer to check their condition if they are not sealed.
If you coach does have an big inverter or a good 3 stage converter, make sure you know how to equalize the batteries (usually an option on higher-end inverters, it also can be automatic).
Run water heater on LP and the furnace(s) to insure they work well (something some people don't think of in the heat of the summer in FL). If you have heat pumps, make sure they heat as well as cool and both fan speeds work (usually at least two fan speeds in roof mounted A/C's).
Make sure to go on the roof and crawl under the coach, I brought a creeper along (plus dishes, bedding, etc for the trip home). Since you're flying you can't bring a lot of stuff with you, nothing that a trip to Wal*Mart, AutoZone, Northern Tools or Harbor Freight (or CW, as GaryKD mentioned) can't solve
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I agree with the I95 routing, note that you cannot go through the tunnels around Baltimore as well as what Gary mentioned about NYC. Also, the parkways (or whatever they are called on LI) are not real RV friendly, I ended up taking lots of local roads to Oceanside when we went by RV. If I remember correctly, the bridges over the parkway are arch shaped and have limited clearance unless you stay in the middle. You may want to reconnoiter your route from the city to insure you don't have any clearance problems
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If you find you have an extra day or so, consider taking the Chesapeake Bay Bridge/Tunnel, they do allow propane (it must be turned off), we did and it was a neat drive. We parked overnight at the rest area at the south end of the tunnel under the main shipping channel, saw a beautiful sunset and sunrise the next day. We continued up 2 lane roads and took a ferry to Cape May, NJ.
As Gary also mentioned, Flying J's are great places to fuel up, you can either use the truck pumps for diesel or the RV island most J's have. They also allow overnight parking. You can stay overnight at rest areas in SC, NC and VA (rules vary, but most states will allow you to get a good 8 hours sleep). A lot of times, we hurry along, not staying in campgrounds for part of the trip so we can slow down and stay in nice campgrounds in desirable locations in other parts of the trip.
Since it is a D/P, you may want to try to get LD to do a full PM, as they can get expensive, and you don't want to get the coach just to find out it needs an expensive PM. I'm sure some D/P owners can chime in on what to ask for.
Good Luck, and have enjoy your new-to-you coach
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Stewart