I presume you mean "no longer non-stop", not "no longer direct", as "direct" means that the plane stops, but you don't have to change planes to get to your destination. Non stop means that the flight doesn't stop.

Regardless, see what your options are on other airlines, at what price, and see if perhaps there is a nonstop on AA a day or so either way of your original flight. Because there was a 'significant' change in your itinerary, you can call them and cancel your flight all together and get ALL your money back. However, your options on other airlines may involve a lot more money than your original flight. So, you may want to see about changing your dates slightly. But AA will NOT pay for your extra hotel nights, no. AA would prefer to keep your money and switch you to a different date, if necessary, so they will be slightly flexible with you. Best wishes..