Typically private universities don’t accept CLEP credits. I am not sure if many accept DE credits either. Or, very unlikely that they will allow DE credits to fulfill any curriculum requirements. It’s probably more likely that your child would be given the option of skipping intro level courses.
At any rate, what they’ve stated is what you have to go with. There are other colleges to apply to if CWRU’s policy is unacceptable.
If the goal is for staring college with higher than freshman standing, publics are the best option.