That quote was from the MA state’s website. 6 months for community college, 12 months for 4 yr college. If you were going to go anywhere to establish residency, TX and CA are both excellent choices.
What options do your parents support? Unless you plan to make your life in Lebanon, staying at AUB (I assume) is not a good idea. And the sooner you move to the US, the sooner you can apply for citizenship. MA, CA, TX are all great options. Unless your mother has very valid concerns, it would be foolish to ignore the opportunity that having family connections in CA and TX offers, because they both have excellent state schools with cheap tuition.
As for transferring to a US school that would give you a lot of financial aid, it’s possible, but you really cannot depend upon this. Better to pick a state, come here now, get an ID, register to vote, get a utility bill in your name, get a job, and work (on the books, of course). Then hopefully finish your associate’s degree in two terms of community college in January and over the summer, and transfer to a state U to start in the fall, and finish your undergrad in two more years - you could even go straight through, doing 3 semesters a year by attending in the summer, too, and be done even earlier.
It doesn’t matter so much where you do your business undergrad. The best state U undergrad business program in TX or CA would be perfectly fine. Then you work for two years, then you get your MBA from a name program, like Wharton, Harvard, Chicago, etc. You’re then equally attractive to any employer, when compared with people who did their undergrad at tippy-top private schools.