I'm all about using a Harmony Director to teach kids to listen to and manipulate pitch. However, I do believe this was a skill people learned before the invention of this marvelous device. With that being said, the HD definitely makes life easier.

To the OP, I am a big believer in getting your kids to sing. You can start with a concert F (or whatever note you want) and have the kids match. Use one of your better players for the pitch reference. From there you can move up and down from the beginning note by half steps, then move on to an expanding interval exercise (i.e. F-E-F-F#-F, F-Eb-F-G-F, etc.). Be creative and don't move onto the next thing until the kids can sing and play what you're asking them to do.

Once they've got that going pretty well, then you can move on to your chorale and get them singing that. Start with just the first chord then get each part to sing independently before putting it all together.

Doing this can be tedious but over time you will find they're ability to listen and adjust on their instruments will improve greatly.

I also remind my kids pretty constantly that pitch and tone are related. Very often I'll isolate a student who's playing out of tune and as they work to get to center, they'll find that they're tone improves as well. Be sure to point that out when it happens.