Okay...maybe a little bit more detailed response...
At this very-young age, I'm not a fan of exercises specifically for strength-building. Focus on mechanics and make sure their bodies are using good movement patterns. Increased strength with inefficient mechanics is not a good path. Build throwing strength by throwing a lot. Playing catch with a partner brings in the accuracy component to throwing (which is also a critical item), and improves glove skills. Hitting balls - tee is okay, front toss is better - with the goal of hitting them as far as they can is always a good thing (at any age).
From 5YO to about 9/10YO the focus should be on mechanics and explosiveness. Get the child to do the arm pattern/swing pattern correctly to optimize the current physical capacity. Then add distance for throwing. Jaeger long toss is a prime example of just feed the arm. If your child hits or pitches, get her to do that as explosive as she can while maintaining proper mechanics. Same thing with hitting. The body has to feel that and the more they do it and begin to understand their bodies, the better they'll become. You as the instructor have to be intentional about it, they won't understand. Doing speed and agility exercises (platforms, ladders, hurdles) help them understand the feeling of being explosive. Now is the time to learn that. It is difficult to learn that once they are older. Once they're around 9/10YO then flexibility becomes a prime focus. The body isn't prepared for strength training until around 16YO on average.
I wouldn’t concern myself too much with strength training at this age. Focus on building motor skills and agility. They will get stronger no matter what and their bodies will handle it better at an older age. The next couple years they learn to be an athlete and don’t underestimate how much that is noticed by coaches in all sports at all levels.
For throwing I would zero in on technique (talked about all over DFP) and add some long toss in (relative to age).
When my daughter started the sport at 8, she was weak with the throw, weak hitting, etc.
Honestly, just playing catch a lot (with good form) and she's now a 9 year old third baseman and the only one on the team that can make that long throw consistently. I never even told her I was stepping one step further from her each month as we played catch in the driveway.
My DD is 9 and one thing that shows up when doing one arm at a time batting drills is her left arm strength (lack of strength). We like to play catch and work on increasing distance until her right arm is tired as well as hitting off the tee and front toss, side toss, etc., but this mainly works on the dominate arm. Any drill recommendations that help work on the weak arm?
I'd keep doing what you're doing lancer. For one-arm drills I went to Walmart where they sell t-ball bats for $7. Picked up a 24 inch one for one-arm drills. I'm not sure many of our 9U girls could do one-arm drills with their normal bat.