What designation should be assigned to a teacher's trainer who is also teaching in the same school?
You seem to have multiple roles. For teaching responsibilities with respect to students you are "instructor" or whatever other designation your institution uses for that. 

But part of your duties are "Instructional Designer" or maybe "Curriculum Designer".

And the third role is "mentor" to the instructional staff or another term with the same intent. In my world, the word "shepherd" would apply, but some would find it odd, perhaps. "Supervisor" only applies if you have some power other than giving advice and counsel. 

But an overall term might just be "Curriculum Consultant" or similar.