The yoga wouldn't bother me. Not being allowed to observe the class would. If they want you in a separate room where you can watch through a window or one-way mirror so your child isn't distracted, I can kinda understand that, but I will never leave my child somewhere where I'm not allowed to observe whenever I feel like it. Her preschool allows parents at any time, unannounced or scheduled, and I drop in whenever I can just to see how she's doing. It's not often since I still have DS at home and he can't go with me, but I like knowing that it's open for me or any parent to come observe.
I've taken 2 yoga classes. One in college which was great. Can't remember which type, although it wasn't raiki. There was no religion or even spirituality to it at all. The concentration aspects were all centered on breathing techniques that helped you calm your mind and body. Folks who needed a "mantra" to concentrate on were encouraged to choose something one syllable (like "ohm" or "mmm") so a message didn't distract their mind from relaxation. The breathing and stretches were designed to calm your mind, help you focus, stretch your muscles, improve your breathing, etc.
The last class I took was called "Christian yoga" and it was taught by a mom in my mother's group. It was really just yoga where she interspersed things like "clear your mind and focus on God who made your body", "thank Him for ....", a few Bible verses, etc. Personally, I think this class was designed for those who, like you seem to be, are uneasy with yoga because it's unfamiliar and was originally used as a spiritual exercise by other religions, even though most people here in the US don't use it that way. By giving it a Christian bent, it becomes something "ok" to participate in for those who were worried about it.