Don't use the music app.

It has a bunch of frustrating restrictions due to agreements Apple has with major copyright holders in the music industry - copying files onto a device is intentionally difficult in order to fight music piracy.

The industry standard for drama is to run QLab on your MacBook - it's free for basic use, and advanced features (such as surround sound or timing a fireworks display to line up perfectly with the song) can be unlocked for $4 per performance. You will probably be happy with the free version.

It's quite easy to use and has all the features you could possibly need wether you just want to play a few songs one after another, or all the way up to the most complex performances (I know someone who used it to run the opening ceremony of the olympic games...)

With modern sound boards, you can just run a USB cable from the Macbook to the sound board and it will integrate nicely. Or just use a headphone cable if you prefer to keep it simple. You mentioned "splitting the screen" - Qlab can run a single performance on multiple Macs, so you and whoever your working closely with can have your own screen each.

You mentioned using a separate account so kids can't access your stuff, Qlab can "bundle" a project so all the song files and everything are together, then it's easy to put it on a USB drive, Air Drop to another Mac, email it to someone, copy it to another account on the same computer, etc. It also has "Show Mode" where most features in the app are locked down and you can just run the performance without screwing everything up.

Whatever problem you encounter, QLab almost certainly has you covered.

If you really do want to use your iPhone or iPad - then the same company has an app called "Go Button" which is basically a light weight touch screen version of QLab. It's quite new and I've never used it myself, but it looks like it might work well - certainly it would be better than using the Music app.

https://qlab.app/

https://gobutton.app/

Try VLC that might be an easier method than the music app.

I’ve had success doing this: https://support.apple.com/guide/itunes/import-items-already-on-your-computer-itns3081/12.13/windows/10

Also worked on MacOS.

Connect the iPad to the computer. In Finder select the iPad under “locations”. Select “Music”. Configure what to Sync, and then click “Sync”.

Alternatively, depending on your use case, it might be easier to simply use VLC and the Files app on the iPad.