* Traveling kindergarten teacher: This is a straightforward and easily understood alternative.
* Visiting kindergarten teacher: This emphasizes the temporary nature of their presence at each location.
* Peripatetic kindergarten teacher: This is a more formal and less common term, but accurately reflects the traveling nature of the job.
* Resource kindergarten teacher: If their role involves supporting multiple schools or classrooms, this might be appropriate.
The best alternative will depend on the specific nuance you want to convey.