[Voralphion]

I believe the main reason for Elrond's reaction to Aragorn and Arwen's relationship was purely selfish. He had already lost one relative, his brother Elros, to mortality and didn't want to lose his daughter as well. Galadriel having an objective perception of the situation would've seen that is was in the best interests of both of them and middle earth so she encouraged the relationship. Also I believe she must have known about it as she had the ability to read people's hearts, and if shhe didn't find out from Arwen, she certainly would have from Aragorn.