Should only need one wheel lock. The important part is that it covers the lug nuts so they can't get the wheel off and put your own spare on. I am sure a good quality wheel lock is NOT cheap. Get the same one the police use, as it is proven to work or they would switch.
Since the trailer tongue is not galvanized I would make the tongue removable. Kinda hard to steal something without chains and a hitch. Plus it will store in a more confined space. Very cheap and simple to buy an inner sleeve, a couple bolts, and a hitch pin. Probably could even reuse the bolts currently holding the ball hitch on. Feel free to use said dull hacksaw to cut the end of the tongue off. I'd use a bandsaw, but an angle grinder will get it done too.