Can you apply for the job you really want with the sister company?
I think like with most companies, because you are already an employee, you can find the hiring manager of that position and explain that you are interested in this position and willing to move to get it.
Possibly even network in your current job to see if anyone knows someone on that side of the business to give you a recommendation.

I think you have a leg up on that job bc u currently work where you do.

Thats been my experience whith my former company.

Good luck!

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