I am moving half way across the US and the trip will take 3 days. It will be in the summer so I guess that is a good or bad thing?
Should I use a small dog carrier, box, or tubaware container
What do I feed her
Does she HAVE to bask?
Im going to be staying in a hotel at least one night and will have to sneak her in so I dont think the sight of heat lamps will work if its an inside hotel.
Im kinda stressing because I know she is going to be super stressed and I want to make this as easy as possible.
How old is she? Honestly, if she's an adult, you could probably get away with not feeding her for those few days, and like you said, she'll be stressed and probably not want to eat much anyway. If you plan to feed her, you'll need to let her bask to digest for at least 2 hours before and after eating. If you do plan to take in her basking lights, you can stick them in a tote bag so they're not visible. Make sure you take her for a few car trips before you go so you can see how she reacts, and so she gets used to being in the car. When I traveled with my boy last summer, he pretty much slept the whole time we were in the car.
Obviously you'll need to take her in with you whenever you go anywhere (you can't leave her in the car), so pick a container that isn't too obviously a pet carrier. I got a pet carrier that looks like a purse, so I was able to take my beardie into restaurants without it being too obvious. I would say just make sure whatever you use is sturdy, secure, and has breathing holes.