Can you claim loss of use for a totaled travel trailer that was your home in an accident which was not your fault?

Yes, in most circumstances you can claim loss of use against a third party. There are a few exceptions, Michigan, for example is no-fault for property damage and you would therefore have to have rental coverage on the policy covering the travel trailer. I would think you would be owed the cost of renting a replacement trailer for the duration of repairs (reasonable repairs) or until you received a reasonable total loss offer.