I would agree that Country_Wife paints a bleak picture of the Lake Louise Campground. While it is located on the train line, it's a beautiful place to camp - and it's one of the only full service campgrounds in the park. The campground also has the Bow River running right through it - with it's fantastic trail system, incredible scenery and possibility of seeing wildlife it could be just the kind of experience you are looking for. While I seldom disagree with County_Wife's advice, don't let this keep you away from this place. I frequently take my children tent camping there - and we've always enjoyed this place.
It's still the busy season in early to mid - September. While I don't think you'll have problems finding a sight, I would anticipate it being busy. At this time of year, the campground will be full of folks just like you who are renting and traveling in their rental RV's.