What were you looking for? A long, complex, complicated response to something that is just that simple? Adam and Eve didn't just hide because they were naked, they stepped out of the presence of God, and freely distanced themselves from God.
Back to the topic, you ask if it is foolish to call God our Father, yet in the basic beliefs of your religion you referred to it says:
"7. The concept of God is represented by two distinct and separate persons, our Heavenly Father and our Heavenly Mother."
http://www.thesongofgod.com/tgc/basic_beliefs.html
Is this a polytheist religion? You believe in God the Father and God the Mother? Are they both one? If they are one in the same essence I can understand, but if you say they are different in essence you believe in (plural) god's not (singular) God.
Your own religion that you believe in states God is our "Heavenly Father," so answer your own question, is it foolish?