Difference between 别人 and 人家
别人 means others, 人家 can mean others or "I/me".

别人 always means other people, that is to be used to refer to people that's not part of the current context.

人家 could mean the same thing. The difference is that 人家 could be used to denote a specific group of other people, i.e. "THE others" or simply "They/He/She", or even "it", which 别人 is mostly used to denote unspecific general others.

And, in some settings 人家 could be used to denote "I/me". This is more commonly used by females or children, often to increase the level of feminine or cuteness when trying to make a requests or complaints. And in some regions the latter usage could be quite common.

人家 could also be used sarcastically to refer to people who you think are pretentious by implying they think they are so cute and nice that they would call themselves 人家 but they are not actually that nice or cute.

In the two sample sentences, "人家" and "别人" could be used interchangeably.

人家都同意，就你一人反对
It could mean "They all agrees, you are the only one doesn't" in the context that a group of people negotiating something and "you" are the only one that has a problem.

It could also mean "Everyone WOULD agree, you are the only one doesn't" in this context 人家 means people other than you, but not necessarily real people who are involved.

And you can use 别人 to archive same effect.