Welcome to our forum. You are just the type pf person it was designed for.
That said, I get the impression that you don't have previous experience with travel trailers. If this is wrong and you are experienced, I apologize for taking up our time.
This is my take on your plans, off the top of my head. If you are inexperienced, I think the first thing you should do is delay your trip at least 2 weeks. A cross country 'shake down cruise' is pretty ambitious, even an overnite in your driveway is better.
Safety is extremely important. To go cross country, I hope you have an adequate tow vehicle with towing package, at least 5000 pound capacity with a 190. Use a bathroom scale to check your tongue weight, get a small air compressor to keep your tires safe. Check your hitch to avoid a 'false hitch' and the trailer lights before leaving each day.
I bet you are trying to go too far, too fast each day. Figure no faster than 65 mph, (I go about 62) and stop driving after 5 hours or so, and plan for a rest day after each driving day, or at least every second day. I know people can drive 10 hours with a car, but the trailer is much harder to drive. Start each day as early as possible, this avoids traffic except rush hour type.
Get the book 'Next Exit' and a good road atlas.
A good trip planner is very helpful. Until they recently ruined it, Good Sam Club had a nice one, I haven't found a good replacement yet, probably KOA has an equivalent one, but get one, it'll help you find your next stop.
Practice using the manual brake on your trailer brake. I do it routinely as I am driving along but that's just me. It is very unlikely, but if the trailer begins badly swaying, you have about 1 second to get it under control using the trailer brake. Braking the tow vehicle is useless.
Dumping the black tank is simple, but if not done right can get you into trouble. Many campgrounds limit the number of vehicles at a site to one and you'll need leveling blocks if you don't have them.
Good luck. In the 19th century, our ancestors made that sort of trip routinely. We have a much easier time now, but we still can have difficulties.