My son did an internship with Oak Park Festival Theater in Chicago suburbs between freshman and sophomore year. There’s a very small stipend (he worked at a donut shop for money mostly) and though all the interns u/s and have small onstage parts, performance opps vary a lot from year to year. He also got some equity points but this is also not a guarantee (you have to have three equity people in your show to get them and sometimes there are only two). It’s worth considering if your kid has a place to live for the summer in Chicago.
There's a lot of crossover, according to parents with kids at both programs. I believe they sometimes cast acting majors in musicals and vice versa, and acting majors get a certain amount of vocal/dance training.
I would go back to previous years' acceptance threads and look for the schools that have lots of acceptances rather than just one or two. These are mostly audition schools, so there are no sure things, but there are definitely some schools that more people get into than others. (No offense to anyone whose school meets this criterion. I would include my son's school, CCPA, in that category, even though I believe that the quality of the program is very, very high.)