Stereo Mic vs. Shotgun mic for theatre production

I am an extreme amateur looking for what I think is a fairly straightforward answer but one I have not been able to find an answer to. My kids are all in theatre (middle school/high school.) I have been struggling for years to get good film of their performances. If I use my Cannon dslr camera, I get great video but horrible audio from the built-in mic. If I use my camcorder I get good audio but the camera can't handle the theatre lighting exposure and I get horrible video. So, finally I took the external mic from the camcorder and put it on my dslr and shazam! Great video with decent audio. So now I'm thinking my money would be best spent on a decent mic for the dslr. But which one? I used a stereo mic at the last play and it picked everything up great, too great, as it picked up every audience sound there was, which is a lot at a middle school play. But I'm afraid a shotgun mic might be too focused. Will it pick up everything on a high school stage from one end to the other? If so, do I have to be placed far back or will it work well from the first row. I just don't know which will work best. Also, if I use a stereo mic is there an attachment I can put on it to block sounds coming from behind the camera? I have searched high and low and can't find anything. If you can help at all with these questions I would really appreciate it. My oldest daughter is starring in Frozen in two weeks and I really don't want to mess this up.

Thanks so much, Suzette