I just traded in my vehicle but would like to still see it's trips. However, I don't want to see it's final location in my app or when I ask my Amazon Echo where my car is. Is there a way to do this or will I just have to live with it like this?
If you delete your car, all its data will be removed from the app and Web Dashboard. You could do an export of that data from the Web Dashboard into a CSV file and see if that suffices for you w/r/t hanging on to that car's history. If it doesn't, unfortunately, the only solution is to leave that car listed in your account. (FAQ: How do I download/export my driving data from the web dashboard?)
The Alexa skill is based on your account so once you set up your new car, it should be included, but as long as your old car is still on your account, it will list that one too. Of course, its location will always be the last known location from your account. Sorry there's not a better way of handling that use-case right now.
Finally, with the new app & Pro adapter, there's no way for you to remove a car yourself. Tech Support needs to do that for you on the backend so if you decide to go that route and are using the Pro, shoot an email to email@example.com.