AOS while on a Tourist visa?

[jmana]

I have a questions regarding the process of getting an AOS with a tourist visa. The reason I ask is I met a woman whom I visited in Russia, and we have a lot in common and would like to see each other more to see where the relationship goes. As part of that she would like to visit here for a few weeks, but I was thinking that if everything goes well I would really like for her to have the option to not have to leave, or the very least to be able to stay for extended periods of time. I was wondering if it's possible to have someone come here on a tourist visa, decide to marry, and file for AOS without having to do the whole process of filling for a K1, then wait several months before we can marry. The only tricky thing is she also has a daughter, and I was thinking to increase her odds of being permitted the tourist visa, that she would leave her daughter with her parents, but if I tell her I want her to stay, what is the quickest route to get both her and her daughter here legally? If I were to tell her she could stay if we get married, and she agrees to it, could we get married, file for AOS, and allow her to return home to take care of her daughter, or would she have to stay here until the AOS is complete, then file for her daughter?? I guess on paper the easier way would be to file for a K1, but with that I feel that once we file the chance of her getting a tourist visa would be next to impossible, and I can't constantly be taking off work to go visit her, it would be better if she could visit me. Plus I hate the idea that once we file for K1 we can't get married even if we wanted to until after the K1 is approved, and she goes back home to complete the whole paperwork, medical exam, and interview process.