<p>oldfort,
Your daughter wouldn’t be a good example to guage. She got an internship experience with a major bank through personal connection. It’d be easier to get another one with that under the belt and if she get anoher, it’s not exactly “by herself”.</p>
<p>OP,
I am not sure if H4 vs F-1 is the problem. Most companies ask “will you now or in the future require sponsorship”; I’d heard that asking about visa type is technically illegal. Did the UChicago system really ask for your visa type? Many recruiters don’t know the difference among different visas and some don’t even know what “permanent resident” is.</p>