My daughter and I have read through a couple more games in Logical Chess and also played a few games the last few days. She has been having a good time, which is the main thing.
She was having trouble seeing knight moves, so I looked up some exercises for her to practice with. One puts a knight and king at opposite corners of the board, with pawns scattered about (a chess maze, essentially); the goal is to check the king without getting captured moving only the knight. She did it for a while and told me it was getting too easy, so I told her to start replacing a pawn or two with Rooks or Bishops, and she kept at it. Over 3 days she made significant gains and is able to point out knight moves a lot quicker.
Tonight I had her playing KNB vs K. I showed her how the mate would look with the king trapped in the corner, scattered the pieces and let her at it. I told her to make sure the Black king fought hard back and didn't voluntarily go to the "bishop's corner". About 30-45 minutes later she worked it out!
In our game last night, she actually had a pretty good attack, but let the initiative slip away and I won the game. I hope to review the game with her and see if we can't find spots she could have improved.
She's also really excited her middle school will have a chess club.