If construction is making my apartment inhabitable and I’m forced to move into a temporary trailer, do I have to pay rent?

If the landlord is providing the temporary trailer, then you would still be liable for rent, though you probably should be paying a reduced amount--i.e. an amount commensurate with the fair rental value of the trailer, which is likely less than what you were paying for the apartment. That is because when there is a landlord-caused impairment of living conditions, the tenant is generally entitled to recover the difference in rent between what he/she was paying and what the premises are worth in their impaired condition; the same logic and legal rationales would have you pay a reduced amount if you are in less desirable, landlord-provided temporary shelter.

If the landlord is not providing the trailer, then you should not have to pay rent for the period of time you are denied possession of your apartment--the landlord is not providing you the space you are renting, and that failure, which is material breach of the lease, then excuses you from your reciprocal obligation to pay rent. Indeed, depending on the circumstances and how long you are excluded from your apartment, you may be entitled to break or terminate the lease without penalty and move out.

(Note: even if the landlord is providing the trailer, if you are denied access to your apartment for long enough--which is not, unfortunately, a hard-and-fast number of days, so there's no easy answer to when that occurs--you would be entitled to terminate the lease because again, the landlord is breaching the lease by not providing what you agreed to rent and are paying for.)

Note that the above assumes the landlord is causing or doing the construction: if you have commissioned or caused the construction, then you would still pay full rent.