TD Visa for common-law in Peru

Hello,

I am currently in the us on a TN Visa. My fiancee is Peruvian, and is in Peru with our child, a 3 year old who has both Canadian and Peruvian nationality. My fiancee currently has a US visitors visa, and no Canadian Visas. Will she be able to come on the visitors visa with our child? Can she apply for a TD Visa even though we are not married? Will my child be allowed to enter the US from Peru with her mother alone? I have no status in Peru. I have been working in Libya for the last year on a 7 in 3 out (week) rotation, and my out time living in Peru on tourist stamps. Since the trouble there I have been relocated to the US office, and will be here probably for a while. Any help or guidance on where to find help is appreciated. Thank you.