Translation:Will we take the subway to the hotel?
能 is more of the physical ability 可以 is more of being allowed to do something, and the example character 会 means more of the skillful ability or knowing how to do a task. I think it should be 能 that is used in this situation because 能 is more like do we have the physical ability to take the subway to the hotel and not 会 or 可以。
No, it is extremely strange to translate "我们会坐地铁去酒店吗？" to "Can we take the subway to the hotel?", because this means "Do we have the knowledge to take the subway?". This sounds like you are a little child, and this is the first time ever you take the subway.
If you want to ask in the sense that "Does the subway lead us to the hotel?", then it would be "我们能够做地铁去酒店吗？".
It can have several meanings, such as the skill to do something eg 你会用筷子吗？ This is generally not asking if someone will use chopsticks or if there is the possibility they will use chopsticks, but rather whether they have the skill of being able to use chopsticks. 你会说中文吗？is also another example of where 会 is also used in this way of skill/ability I think in the example given "我们会坐地铁去酒店吗" will would probably be the most common translation. Given that it's in question form, I think " will" and " the possibility of something happening" are effectively the same question.
Actually subway, underground, tube and metro (and probably couple more) are all the same depending on the country. In London the transportation system is called underground and everybody refers to it as underground (or tube). If I wanted to play your game I would say that subway is an underground passage not an underground train.