I think you can figure out the ahead or behind thing. What you have to be wary of is over terraining her by taking her to slopes too hard for her at this point in time. Individuals pay me $100's to fix their childrens really big wedge that the child is stuck in. Interestingly enough, the parent caused the braking wedge in the first place by taking the child to slopes too hard for them and the result is the huge V. I can usually fix it in an hour or two (of private instruction), but it comes right back if the parent takes the child back to the "scary hill" again. The child will often , "when asked" choose the slope again to please the parent. I always tell the parent after the lesson where (what runs) the child should be skiing. It becomes a big setback in the child's development when defensive tactics are adopted for survival on steep slopes. So, always encuurage turning to stop, not just "pizza", gliding and controling speed by turning (skis making a circle in the snow).
As for the lift, if possible on a triple or quad, see if only the two of you can load. Nothing like a clumbsy adult impedeing the loading process for you two. Also, always have the child on the side the attendant is standing, so if the attendant needs to assist in loading the child, you are not in the way. I often motion for the liftie to slow the chair down a little, so I can assist the child to the loading place and make shure the child is on the chair safely. I always make shure the child gets off the chair on the unloading platform at the right time by lightly holding the back of the jacket by the sholder to neck area. On really crowded times, you might have to load with one or more other people, if that is the case, look for someone to share the ride with that looks like they have skiied quite a bit before, rental equipment is a good clue that the person is not a frequent skiier and may give you problens with loading and unloading.
As for blue trails, only very easy ones (if any after reading what I posted above) that have no steep spots. It is as likley to get hit by an out of control skiier there as anywhere, but maybe going faster than on a green.
I hope this is helpfull, I teach hundreds of children every year and know the ropes.