Can you use the verbs "will" and "would" in an if clause?

All 3 are correct, but the first would much more likely be "...I would be so happy" in common context. There are a number of peculiar times when "would" can be used in an "if" clause. Your teaching is essentially wrong. BUT what she says is the more common expression in English. Examples to the contrary: "If you would just shut up, I would get some sleep" [More common]: "If you shut up, I would get some sleep" "If he would consider eating some more, he wouldn't be so skinny" [More common]: "If he considered eating some more, he wouldn't be so skinny" Consider also these 2. They mean the same thing but are expressed differently: "If you ate it, I would eat it too" past -> conditional "If you eat it, I will eat it too" present -> future "would" is the verb of uncertainty. If the following verb may or may not actually be occurring, would is used. Including "if" clauses. In Spanish, I can't think of a single example where the conditional tense is used in an "if" clause...so no. Don't think so.. Conclusion: Yes, you CAN use will and would in an "if" clause. BUT it is rare and unusual to do so.

Si vas conmigo a la fiesta, estaré bien contenta. Si no te molestaría, me gustaría ver mi habitación. Si ella hubiera bailado, hubiera disfrutado muchísimo.