My first question is does the trailer have a commercial license or a regular license? If you don't have a commercial license you may be in violation of state department of transportation laws should you put any type of lettering or logo on it.
The second question is how do you plan to use it? Is it going to be just a "general" construction style trailer, a dedicated cleanout / insultating trailer, or something else? Should you decide to label it and are concerned about clients getting a negative impact from it try to keep it as generic/basic as possible.
For instance, if it is going to be general use, I'd go with a copy of what's on your truck on both sides and the back door for advertising purposes. If you're really concerned with it, take off Wildlife Control and people with probably think that you are a portable dog grooming service.
If it is dedicated to a specific construction task such as attic cleanouts, I'd go with the logo (without wildlife control) but I'd also add to the right "Attic Remediation Services" or something generic along those lines with contact information underneath it.
If it will be dedicated to potential "hot" topic items such as portable gas chamber, carcass hauling, or something along these lines I'd leave it blank.