This is to be expected due to the low dynamic range common to cheap point and shoot cameras. The dynamic range is the difference between the darkest and brightest part of an image that the sensor can capture. Something like a sunrise or sunset has a very bright object in the middle surrounded by very dark objects (the darkening sky and terrain).
When figuring out the exposure settings, the camera tries to guess what should be exposed properly, often using an average of the overall brightness of the image however if the dynamic range of the scene far exceeds the dynamic range of the sensor, the exposure chosen may be in the middle between the brightest and darkest parts such that the camera doesn't capture detail in the darker parts because they are near black and doesn't capture detail in the bright parts because they are too bright and become white.
Using Sunset mode likely tells the camera to focus on the darker parts of the image to capture the detail of the landscape, but the sensor still isn't capable of capturing details of the bright part.
One trick you might be able to use to get around this is to "bracket" your shots. If you can use a tripod, you can take a photo with the background properly exposed, but with the sun very bright and then take another photo where the sun is properly exposed, but the scene is very dark. A third photo that is in between those two can also be helpful. You can then use HDR (high dynamic range) software to combine the two images in order to use the detailed area from both of them. Higher quality cameras have a wider dynamic range and thus have an easier time capturing scenes that have a high dynamic range.