The problem with antibiotics and the birth control pill occur because both are administered through the digestive system. Antibiotics cause the pill to flush through the system before all the necessary hormones are absorbed into the body, making the pill less effective. Because the shot it injected, it completely bypasses the digestive system and is not affected by antibiotics.
I do not know of anything that can reduce the effectiveness of the depo shot, other than taking the shot late or missing a shot. Instead of trying to sneak around and get her pregnant, the two of you should be mature enough to tell her parents what you intend to do and refuse to get any future shots. If you are too afraid to do this then you are probably not ready for the responsibility of parenthood.