"Squish the bug" and "leaning into the pitch" are not hallmarks of a proper rotational swing.
"Squish the bug" may work as a cue to get some hip rotation into the swing, but it is a cue that is largely misinterpreted.
In a proper rotational swing, the back foot will come up on the toe and perhaps even leave the ground. But it is not "squishing down". Rather, it is coming up as a reaction to the forces generated in the rotational swing.
If you are pushing down with the back foot and "squishing down" to initiate hip turn, you are leaving a lot of torque on the table and not getting full benefit of the power of rotation. In fact, this is referred to as "reverse pivot" and it is detrimental to generating maximum torque.
The rotation should start with the front side pulling the hips, not the rear pushing them. As the power of your rotation goes forward (around a stationary axis), the front leg stiffens and resists this forward torque.
The back foot coming up on the toe is not the cause of the hip rotation, but rather an effect generated by the the front side pulling the hips through.
The body tilt of a good rotational swing should be slightly back, not forward. Watching video of elite hitters, be they major leaguers or college softball players, will verify this posture in the rotational swing.
Mom101, as a first year player, your nine year old is trying to master one of the most difficult tasks in sports- hitting a moving ball with a bat. Add in the excitement of the game, the nervousness of performing in front of family and friends, and the newness of this difficult skill and many beginning players find hitting in games much tougher than hitting in practice.
At this young age, I would not try to be too technical with my instruction. Keep it simple and try to give her a good foundation with a few fundamentals that are common to a good swing.
Do a web search (Google) for "rotational swing" or "hitting mechanics" and you will find many, many sites dedicated to batting techniques.
One of the most basic videos on rotational hitting, using easy to understand terms and geared toward beginning players, is "Beginners through Little League: Explosive Rotatioal Hitting". Here's a link:
http://www.sportstechnique.com/
On the most basic level, start in a balanced stance. Before swinging forward, a slight loading should be achieved by pulling the hands back toward the catcher. Minimize the stride into the ball with the front foot. The front foot may not even stride forward at all. It can be moved slightly or picked up a bit and put down to initiate the hip rotation.
Keeping the hands back, turn hard with the hips so that the belly button is facing toward the pitcher. Then, bring the hands around, meeting the ball with hands in a "nuetral" position (bottom/front hand palm down, top/back hand palm up).
The hands should follow a tight circular path. Slight bend in the front elbow is acceptable. The back elbow can have a bit more bend and may even come in close to the rib cage.
Follow through after making contact, bringing the bat around the front side of the body. If the wrists are rolled over, it should be after contact with the ball.
The plane of the swing should match the plane of the pitch (the angle relative to the ground).
Practice, practice and practice some more! Use the batting tee, face live pitching and go to the batting cages, all the while concentrating on the fundamental aspects of the swing. Try to make sure that the live pitching in practice is close to the same speeds that your daughter will see in her games.
Seeing many pitches and taking many practice swings, while using correct fundamentals, is the best way to acustom young players to the art of hitting.
Best of luck with your first year in fastpitch!