很简单.be都做了系动词
i wanted to be with my family.
i didn`t want to be alone anymore和
i`m not sure i want to be aloe.的 to 后面都不能直接后面的形容词和副词作宾语.to 后面一定要接动词原形.(固定搭配除外 如look forward to + 动词 ing 形式)
所以be在这里起了动词连接的作用.使得后面做 want to的宾语.
some people don`t mind being alone. i do
同理,因为mind(介意)后面接动词ing形式.所以这里用being