The palace jump is kind of tricky. It doesn't always jump to the largest city. There are a couple of factors:
1. Largest city with people of YOUR nationality. So a size 4 city with all of your citizens will be more favored than a siz 5 city that has 3 of your citizens and 2 foreigners.
2. Culture. The city with higher culture will be more favored.
3. Size 3 +. If no cities are size 3, then of course it will go to a size 1 or 2 city.
So you would be pretty much guaranteed to get it to go where you want if the target city is the largest (no foreigners), highest culture, and is at least size 3. You should practice the palace jumping before trying it in a serious game.
To abondon city, set it to build a worker or settler. For worker, you want the city at size 1, and settler, the city at size 2. Then micromanage the tiles so you have -zero growth-. Then when you complete the worker/settler, you will be asked if you want to disband the city. When you disband the city you will get a worker or settler in place of the city. Or if you have the latest patches, you can just right-click on the city and select 'abandon city' (but you won't get a worker or settler).
Abandoning cities you just captured is treated the same as razing for your reputation. If all (or majority) of the citizens in the city are foreigners, it is still kind of considered a city of the opposing civ. Once your citizens outnumber the foreigners, you can abandon it with no rep hit. Not sure what happens when there is an equal number (1 foreigner, 1 of yours).
If you really don't want the city and don't want any rep hit, donate it to another civ, or add your own workers, so your nationality outnumber the foreigners then abandon it. I suppose you could also leave it as a size 1 city, leaving it undefended, then get another civ to attack it and raze it (but declaring war, may not be good for rep, either).
