Engineering generally is not a field that is highly school-prestige-conscious, though on-campus recruiting can favor larger schools, well known *for engineering/i schools, and schools local to employers (e.g. Wichita State and Alabama - Huntsville for aerospace).
Since you did not name any of the colleges or the kind of engineering and employment that she is interested in, no one can even guess if any of the colleges would offer any internship or first-job-at-graduation recruiting advantages.
She should check carefully whether she is directly admitted into the engineering major of choice, or if she is admitted into a first year pre-engineering program (as is the case for all engineering frosh at Purdue, Minnesota, Texas A&M, and Virginia Tech), or general admission not in engineering (sometimes happens to applicants at schools like UIUC and Washington who do not make the cut for direct admission to the majors that they apply for). If she is not directly admitted into the engineering major of choice, or if she may change majors, she should check the web sites of the schools to see how difficult it will be to enter or change to her desired major.
If he a “naturally” frugal, then it is likely that money will be less of a constraint on his career choices (and anything relating to career choices, such as college major choices), since he is less likely to feel that he has to chase the money while compromising other aspects of the decision.
It sounds like your daughter has many good options, all within your budget or even under budget. I still wouldn’t bargain with my kids for them to keep overages, but that’s the reality of my budget and yours seems a little more elastic.
For both of my kids, studying abroad was cheaper than studying at home. Their college tuition was 20k+/semester, while their study abroad schools were around 10K/semester. Their school allowed us to pay what was charged by the study abroad school, that may not be the case at your kid’s school.