Immigrant or non immigrant visa for my girlfriend & mother of my daughter

Options: K1 Fiance Visa - have her come after approved by the Consulate and given a visa, and then marry within 90 days (strict regulation), and the promptly file an adjustment of status application in the U.S. to receive conditional permanent residency. Your child apparently does not need a K2. The U.S. passport indicates U.S. Citizenship. If there was a doubt, the child would be a derivative beneficiary on the same visa, a K2. The Conditional Lawful Permanent Residency has a two year period beginning from the date of the marriage interview by USCIS in the US if successful. That interview may come typically 3-9 months after the adjustment of status filing package has been receipted. (This time varies-- no crystal ball). The form I-129F is used to begin this process. If you are a "reader" basic information is available on the U.S. Embassy Page for your country if there is an embassy there. Another option that was created during the "Life act" legislation was a quick fix, K3. K4 is for the derivative children. K3 some would argue, is there because it was taking much longer to bring a US citizen's spouse over to the US than a fiance! Of course, part of the delays are sometimes caused by the applicants-- not gathering enough supporting documents, correct paperwork, etc. following the specific rules and getting them in-- or having complicated or not so complicated red flag or potential inadmissibility issues that must be dealt with. So, the K3 allows you after you file the K1 and it is approved, to file that or proof of that, then, with the K3 application. The K3 allows you to have the US Spouse enter and then Adjust Status in the U.S. (There may be more than one acceptable procedure on the K3). Also, without the K's (hybrid non-immigrant- adjustable to immigrant when in the US) visas... there is the option to file an immigrant visa package lock-stock-and barrel at the Consulate. This would allow you to marry, and have the visa processed, and then, enter the US-- and the two year lifting of conditions off the Lawful Permanent Residence would lie ahead-- there are various requirements with time people met, and years of marriage. This is only a general overview of the process, as it is anything but quick and easy. This year, for the first time ever, some marriage petitions moved through the USCIS in some regions in just a few months-- however, some of them were what we call a one-step, which is where someone entered on one visa, and then was able to adjust and file the I-130/I-485 package, such as from an F or H. The reason the Consulate rejected the B1/B2 is what I advise... that if it is viewed as requested to be used to immigrate (immigrant intent) it will be refused, or worse, when processing viewed as fraud. This may be rare, but why take the risk? When the USCIS notices the history of a relationship, the facts may indicate that the B1/B2 in no way is being used to visit but is being used as chicanery (manipulative-trickery) to circumvent the more difficult and lengthy process in place. So, what should you do? You have a sick mother? Why not marry and process for the Immigrant Visa there? That way, you mother can be looked after, and you can be together, or visit them until you get the matter sorted out. You could do the K's-- but at least w/ the IV you have it in your hands before entering and waiting for the AOS marriage interview, so in some ways that could be less stressful.