I am so sorry for your and your children’s loss.
If you run the NPC on the private universities on the list so far, without the one-time payment but your income only, what do you see?
Wrt Barnard, it’s fully integrated with Columbia except for the dorms (which are single sex rather than coed). The key academic difference is the core at Columbia vs. Distribution requirements at Barnard. So, even if she isn’t interested in women’s colleges, it could still interest her.
Have you gone on East Coast College tours?
Seconding Pitt, Michigan State, GWU and American.
She should always apply to the Honors College e, especially at public universities. This could unlock special opportunities and special scholarships.
At American, she should definitely show a LOT of interest. That means creating a college inquiry-only email and joining their mailing list then checking their emails at least once a week and clicking on links of interest (this will be tracked by each college). The info she reads can be added to pages where she jots down notes about whatever struck her and in turn she can use the relevant info for the “why us” essay.
U Minnesota would be less expensive than UWisconsin and very Urban. In addition, it offers one if the much sought-after Critical Language Flagships in Chinese.
If she likes Madison, not a big city but more of a combo political capital/college town, it opens up more locations to suggest :).
What about William&Mary, would it be within budget for you (likely no merit, expect full price)?
What about GMU? Georgia State?
Wrt Michigan State, check this out:
https://jmc.msu.edu/
If you run the NPC on Northeastern (Boston), Boston University, or Boston College; UPenn (Philly); is one affordable?
They’re all quite different but all offer strong Poli sci.
If she’s willing to entertain the idea of a smaller college, Dickinson is excellent for Poli sci and Mandarin, Vassar, Middlebury as well (reach for everyone and rural so academically what she wants but not location-wise).
SUNY Binghamton (nowhere near a big city but one of NYS’ flagships) will give her a lot of credit for the full IBD as will UMD-CP (1hr to DC).
She can also check out the Critical Language flagships, which lead to the highest possible level in Chinese alongside a major. Their graduates are highly sought after. Beside UMN Twin cities, there are
https://www.thelanguageflagship.org/chinese