Sentence Correction

1. Why is "large amount of money" wrong?
2. Is this a wrong sentence, if yes whats the error
"Because they are so similar, it is very difficult to distinguish between X and Y"
Isn't "distinguish between X and Y" a correct idiom.
3.Which is right
"Your sister is so beautiful compared to you"
"Your sister is so beautiful when compared with you"
(Though the first one seems more right to my ears, I was going by the definition in on of the grammar books and got confused. Compare with is used to place two things side by side for the purpose of examining their similarities or differences. Here aren't we placing the quality of beauty of the two sisters side by side and comparing it)

1. "large amount of money" isn't wrong.

2. distinguish between x and y is correct as is the sentence. You can also say distinguish x from y. It's the same.

3. Both are mean, and both are correct. I understand the confusion with which one to use, but it depends on the situation. If two sisters were standing side by side, or you are holding the picture of one and looking at the other, then using "with" is perfectly acceptable. If not, then "to" would be better.