Sunday River is one of my favorite places in the East to ski. My opinion is that managing things with a family is best if you are staying on the mountain. The accommodations can be quite funky, but the convenience of being on the slopes outweighs this.
Navigating from peak to peak can feel a little daunting, but I don't think that it takes much time to figure out how to do it. I know the mountain very well, so I find it quite easy to navigate from peak to peak. One of the nice things about Sunday River is that most of the lifts are 'top to bottom', and you can get to the bottom of one peak from the top of an adjacent one. The exception to this is Oz and Jordan Bowl -- I usually stay in the South Peak area, and I find that getting to Jordan Bowl is something of a "commitment". When you arrive at SR, you might want to talk to someone who works at the mountain (or a local) for some pointers in navigating around.
I have never been to SR during President's week, but we used to do a multi-family trip every MLK weekend. It was fairly crowded, but (as with any crowded place), there are ways to minimize waiting for lifts. I used to scoot out on the mountain early, when the lifts first opened, and ski for 1 to 1 and 1/2 hours. By the time I got back to the condo, the rest of the families were about ready to go out. We would time lunch to avoid crowds and maximize ski time, and late afternoon is often a time when the crowds thin out. You can see why this strategy works well if you are staying at an on-slope condo. The busiest time of the day always seemed to be mid-morning around 10am and at the lifts by the main lodges. Once you get up the mountain, then the crowds seem to spread out.
We haven't used the ski school in several years, but it compared favorably to other mountains that my family has been to (and we have been to many).
I know that this is a very broad-brush set of answers but I hope it helps.