I am not a teacher.
The final "to" is not needed. The previous "to" is still in force.
Personally, I would use two sentences.
"Please pull the power cables from the control room, through the wall to the living room, and then run it under carpet. Then run it the inside wall cladding to where the LED display panels are to be relocated."
You might consider separating the sentences with a colon instead of a full stop. (... carpet: then ...)
[I do have a Diploma in Software Documentation, which has been accepted by employers as evidence of competence as a technical author.]