Reasonable means that whatever decision was made is appropriate given the particular circumstances, and most would regard it as so.
Justified means that whatever decision was made is done for a good reason, in the interest of fairness.
There are times the words could be used interchangeably, and contexts where the difference is subtle. It all depends on the nature of the request or issue at hand.
I might use "justified" if I was angry about something, and was acting in response:
Was it polite to skip their wedding after they insulted me like that? No, but I think my decision was justified.
I might use "reasonable" if I think everyone would agree that there was nothing else that could be done:
Was I happy about missing their wedding so that I could go to my mother's funeral? No, but I think my decision was reasonable.
But there are contexts where either word will work just fine:
You said that you'd deliver the cake before noon, but it didn't get here until 3 o'clock. I think my request for a refund is reasonable/justified.
In that sentence, reasonable would work because most people would agree that a refund would be appropriate given the circumstances, and justified would work because the request is fair.
There are two types of relative clauses in English, which I shall call 'defining clauses' and 'commenting clauses'. They are best described with an example:
Pilots who have dull minds seldom live long
Pilots, who have dull minds, seldom live long.
The first sentence is a warning about the dangers of having a dull mind if you want to be a pilot. The second is insulting to all pilots.
Defining clauses are never separated from the main sentence by a comma: commenting clauses always are.
There's an old fashioned rule that you should always use 'that' rather than 'which' when you are writing a defining clause. Thus
Animals that lay eggs are called birds.
is grammatical, while
Animals which lay eggs are called birds.
is ungrammatical. These days, however, prescriptivism (language rules) is unfashionable and people are far more likely to consider both sentences to be grammatical, and to mean the same thing. Moreover, in colloquial speech, and even in writing, the rule has never been universally followed.
Of course, neither sentence is factually correct: a snake lays eggs, but is not called a bird!
Best Answer
The two expressions are fairly close in meaning and can be used interchangeably with the following nuances:
"force an idea on the others" implies that the idea was opposed by the others but through some sort of aggression (verbal or otherwise), the others had to accept the idea.
"impose an idea on the others" gives more of an impression that the others didn't want to go along with idea for whatever reason but acquiesced though they might feel there was either some coersion or at the least, an obligation to accept the idea.