In the first sentence, it is me being happy and in other sentence, she is happy. "freuen" is self-reflexive verb. So using "mich" in first sentence is understandable. Why don't we use self-reflexive "sich" verb in second sentencec? Again, here why it is used, "dich" instead of "du" or "Sie"?
It makes me happy to see you in the party.
"Es freut mich, Sie auf der Party zu sehen."
It makes her happy to see you in the party.
"Es freut sie, dich auf der Party zu sehen."