Ha!
This happened to us with DD's daycare. I mentioned to her teacher that she was starting to pick up some sight words at about 20 mos... and her teacher said "yeah, it's pretty normal for them to start identifying things on a page"... A few months later she was reading a counting book and DD counted backwards and her teacher mentioned that "she does that every time and it blows me away! did you know she cant count backwards?"
I just said that DD is running out of ways to surprise me.
I too would question an abundance of 3 yo that can read fluently, unless the program is a magnate for gifted kids, which is possible...
As far as your daughter, as others have said, follow her lead. Let her play on tablets/leap pads... I do with my daughter and I have seen her work out some motor issues and frustrations with it. Too much will be based on your child, though encourage a variety of things.
One of the things we did in our home is make sure that all the bottom shelves of book shelves had children's books. There are 6 book shelves in our house, one in her room, one in ours, and 4 others around... any room she goes into has reading material for her available and accessible. I don;t consider this pushing, as a request to read is one I get several hundred times a day.
I hate the idea that there is a prescribed amount of anything that is just right for a child. Parent the kid you have, not the one people think you do.
she sounds awesome.
