My recommendation to the OP based on our last year’s experience:
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Do not apply to state schools except may be some specific southern states and some Texas Universities. But in these demographics may be of concern. In general state schools will not give financial aid to internationals or even to OOS largely for that matter. Admission here will be in some sense easiest to get because you will be full pay and they don’t care about yield.
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Apply to need blind + need met private if you believe your financial capability is really low. It may be hard to convince them considering divorce situation etc. Generally for internationals it is tougher deal to come through in a complex situation.
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Mid-ranked need aware private R1 and mid rank LACs (30-100) may be the best bet. Take a look at their common data publications and see what is the average merit+need based they have given for internationals in last couple of years. Generally you will be within +/-20% of that number if you get admitted.
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Apply to places where Biology, Biochemistry and Chemistry constitutes a sizeable population of students. Some LACs focus more on social science even if they have these departments.