My daughter often forgets to press the clock, and her opponent is using her time to think. Is it against rule?

No, it's not against rule. Keeping clock time correct is both players' responsibility. Her opponent has no obligation to remind her, and no one can remind her according to rule. She has to learn the lesson the hard way.

But it's against sportsmanship if you notice that your opponent has forgotten to press the clock but not remind him/her. Even worse, if you pretend that you are thinking on your own time. No one would like to have you as a friend if you have been caught. Yes, it's not against rule, not cheating, but it's very close to cheating in many people's eyes, especially from the victim's point of view. It will damage the honesty and fairness of the game.

If a coach teaches his/her student such cheap tricks, s/he is doing a disservice for nurturing the child's character.

I actually encountered such a child once. Her chronos clock has mechanical problem. Normally a light tap is enough. Hers required hard hit. She didn't remind me about the problem. At multiple times she just sat there, pretending. By looking at her, I knew something was wrong. After the third time, I began to crash her clock and also crash her game. I didn't feel good about the girl, and I despised her coach even more.

NOTE: your opponent is not allowed to make a move if you don't press the clock.