kid not interested in college visits - should I insist?

It’s much better if she visits. Especially the ones that will be safeties. A NM student who is applying someplace that gives merit money has to show interest. Otherwise they could very well reject her to protect their yield. I know very high stats students who were rejected from Tulane and University of Miami. They were in the top 25%, but did not visit and therefore could not give a good reason why they were so interested in the school.