Another great way is to build hand eye coordination is tossing a very soft small nerf football.
I played a lot of catch with my daughters in the back yard.
Throwing helped build muscle memory for the co-ordinated movement that could be transferred to tennis.
Over time, they learned to catch it from being thrown further and further, higher and higher, and then on the run.
Then they progressed to overhead catches while running like an NFL receiver.
All in the backyard with very short session, but a ton of fun.
I am sure this helped later in judging the speed of a moving ball, and having confidence to run with an eye on the ball.
The least expensive batting T is a plastic set putting a whiffle ball on top.
Hitting that ball trained their eye to hit it with something as narrow as a whiffle ball bat.
Again, a ton of fun right in the back yard.
Great training for taking a real swing, not just blocking the ball with the racquet (which is what a lot of kids become preoccupied with).
The whiffle ball bat is so light that learning the correct baseball/tennis swing of aiming the butt at the ball, with a late release of bat/racquet head is easy.
And you can progress to hitting a thrown ball with a whiffle ball bat - great training later for hitting the sweet spot on the racquet.
Continue to keep it fun as she improves by challenging her to hit your best pitches - your fastball, curveball and knuckleball. (Obviously don't let on you only are throwing all the balls at the same slow speed, just using exaggerated windups to keep it entertaining.)
I bought a really cheap toy tennis net when they were small and tossed balls to them in the driveway.
Again, a ton of fun right at home.
And you can do a 10 minute session in less time than it would take to drive to the courts and back.
And it is one on one time with just the two of you.
Get out in the back yard and kick a soccer ball around. Encourage her to play soccer to develop the skills to start quickly, stop on a dime and change direction as she plays defense.
No better way to develop tennis footwork.
Get one of those cheap toy baskets for the driveway to shoot at.
A ton of fun.
If she develops an ability to shoot a basketball at a real basket over time it will take a great leg push off to reach the basket.
Great training that the whole body is used to power a ball - obviously essential in tennis.
Tennis is hard.
That is what makes it such a challenging sport to improve at and get really good at.
It is a rare child that will find it fun to make all the progress in learning to play tennis with only tennis as their way of acquiring all the skills used to play it.
That is likely for later.
In the meantime, have a ball!