Did she have to actively pursue the co-op opportunity?
She was incredibly lucky. Her academic advisor emailed the listing to her and told her to apply for it. Her scholars advisor coached her through the application (reviewed her resume, gave feedback, provided a recommendation) and had a quick phone interview which they told her she’d be getting the offer. She didn’t pursue any other co-ops because she liked it.
I have a current ChemE there and he’s picked up his co-ops (none rotating) at the career fairs.
Engineering Career Services has a lot of resources https://ecs.osu.edu
Did your student have issues with sequencing courses due to the co-op?
They usually offer almost everything Fall and Spring, but Summer was harder especially since she’d already finished her general electives. You can work with a faculty member to schedule ‘for credit’ undergraduate research and use that as a technical elective. She did that to get to full time for her scholarships. Her brother has taken graduate level courses for technical electives so that could have been another option. Or she could have scheduled something she was interested in even if it didn’t fulfill a specific requirement.
Was it during summers?
Her co-op was Spring, Fall, Summer. Oops, I realize now I think she may have only co-oped 3 semesters, she did work there after graduation, too. Housing was challenging with all of the moving. But there were a lot of co-ops from lots of schools. Her friend from hs also was there from UCincy. 
Was she still able to graduate in 4 years?
Yes because she brought in a lot of dual enrollment credits.