Let's start with the statutory rape charge. Here's the statute (as of 2010):
14‑27.7A. Statutory rape or sexual offense of person who is 13, 14, or 15 years old.
(a) A defendant is guilty of a Class B1 felony if the defendant engages in vaginal intercourse or a sexual act with another person who is 13, 14, or 15 years old and the defendant is at least six years older than the person, except when the defendant is lawfully married to the person.
(b) A defendant is guilty of a Class C felony if the defendant engages in vaginal intercourse or a sexual act with another person who is 13, 14, or 15 years old and the defendant is more than four but less than six years older than the person, except when the defendant is lawfully married to the person.
Looks like statutory rape doesn't apply since you are not more than 4 years older than she.
I don't see breaking or entering as applying to you either:
14‑54. Breaking or entering buildings generally.
(a) Any person who breaks or enters any building with intent to commit any felony or larceny therein shall be punished as a Class H felon.
(b) Any person who wrongfully breaks or enters any building is guilty of a Class 1 misdemeanor.
(c) As used in this section, "building" shall be construed to include any dwelling, dwelling house, uninhabited house, building under construction, building within the curtilage of a dwelling house, and any other structure designed to house or secure within it any activity or property.
I'm not sure that the trespass charge is sustainable against you because you were invited by a member of the household.
Are you charged with First Degree or Second Degree Trespassing?
14‑159.12. First degree trespass.
(a) Offense. A person commits the offense of first degree trespass if, without authorization, he enters or remains:
(1) On premises of another so enclosed or secured as to demonstrate clearly an intent to keep out intruders; or
(2) In a building of another.
(b) Classification. First degree trespass is a Class 2 misdemeanor.
14‑159.13. Second degree trespass.
(a) Offense. A person commits the offense of second degree trespass if, without authorization, he enters or remains on premises of another:
(1) After he has been notified not to enter or remain there by the owner, by a person in charge of the premises, by a lawful occupant, or by another authorized person; or
(2) That are posted, in a manner reasonably likely to come to the attention of intruders, with notice not to enter the premises.
(b) Classification. Second degree trespass is a Class 3 misdemeanor.
You're going to have to prove that you were invited and weren't ordered to leave before the father called the cops. You could have a problem if he told you to leave and you didn't head for the door right then.
Either way, I strongly suggest that you have a lawyer when you go to court.