Thanks for the file, spencerokada!
If I get the idea here correctly, the following link might describe best what you are looking for.
https://help.maxon.net/#TCARIGPART-ID_CA_RIGPART_TAG_GROUP_INSERT
If you insert “under” as in “Last Child”, the movement from the Jaw is taken, but will allow for the tongue to move on its own.
In this way, the Skin Object needs the tongue “weighted” exclusively, so you gain control over it in the way you like.
To get to that field, click on your Jaw Controller in the Editor View, then show active (Character Object> Display> Manager) in the Attribute Manager.
Image:
https://www.amazon.com/clouddrive/share/xMDLyhgr2tgS1Woh3KjkqmE8ozWmfleqaon6edk20nH?ref_=cd_ph_share_link_copy
The reduced scene I have created here (see below) shows then the Jaw_con Spline. Right sided to it is the Component- the yellow © icon.
Click on this and have a look in the Attribute Manager.
Scene file:
https://www.amazon.com/clouddrive/share/OxImskB31fnZcpz0jWaZBgXebPWXffgvOQopzfLGfE1?ref_=cd_ph_share_link_copy
I hope that works for you. Based on the complexity you have mastered already, I guess these steps should be easy for you.
All the best
P.S.: for more in depth and first hand information, have a look at this series. I link part four here as it is the one closest to your question.
https://www.cineversity.com/vidplaylist/creating_a_custom_template/creating_a_custom_template_part_4