Speed really increases a jump's distance much more than the height. It does nothing for rotation - it actually increases resistance. To increase height, the skater has to jump higher (duh) and stay aligned properly through the in-air phases of the jump.
For proper technique, the line jumps are much better for the very reason that you can't use that momentum and you have to rely on proper technique. Doing a jump from a standstill isolates the transitions and forces the skater to align themselves much faster, which is a good thing. That in and of itself increases the speed of rotation without needing additional height or distance.
She's leaning slightly forward (breaking at the waist) instead of stepping up into the air with her upper body over the hips. (On the second one, she actually looks down as she jumps, which increases the break.) If she focuses on leading with the chest or bellybutton and staying up straight, she'll get the rotation she needs without having to increase the speed. That might also resolve the free leg swing, if that's really an issue, because she'll be aligned more strongly over the takeoff side without needing to compensate for the off-balance position.
On a waltz jump, the correct posture is with the free leg kicking through straight. Most coaches add the bent-knee version later, to prepare for the axel prep. Honestly, the beginning skater usually does a hop when you teach the bent-knee version first, which is not the intent of the jump - you don't get them to roll up off the toepick of the skating foot if they've posed with the bent knee in front. They can easily hop off the edge and do a 1/4 turn or less onto the other foot. Better to start with the free knee and then teach the bent knee. Slusher recommends teaching it sooner, rather than later and I've adopted that methodology as well. Skaters should be capable of doing both if they've truly mastered the jump.
The OP's daughter is doing just fine and I'm sure the jump's improving by leaps and bounds as she's had practice and lessons since the video was recorded.