Can I legally move someone else’s trailer that is blocking my easement on a shared driveway?

Probably, yes, but you should do it carefully and with appropriate documentation (usually photos or video).

As a general rule, an easement owner must be given reasonable access to their easement. Blocking an easement is much like trespassing, and in most jurisdictions you are legally entitled to use “self help” (i.e., moving things) to remedy a trespass.

However, the personal property that is trespassing (here, the trailer) is still that person’s property, and you are obligated to take reasonable care of that property and are responsible for any damage. So I would recommend trying to get the owner to move it first, but if you must move it yourself, you want to have proof ready in case there’s a damage claim down the line.