Depending on where you live, that should be enough. I used one of those online a/c calculators, and with some assumptions about the insulation found your peak cooling load on a summer afternoon in Florida with three 1kw lights to be about 16k btu. If you live in a cooler part of the country it will be less. That number presumes no cooling fans on the lights, so if you install comprehensive ducting and fans you should be fine with a 10k btu a/c unit. Of course, it will have to have its hot air exhaust ducted out, as well.

Speaking of lights, can one effectively use 1kw lights in a space less than 7' tall? Even with the light right up against the ceiling you will have only 6' under it, which doesn't leave much room for the plants. Also, you'll need a walkway down the middle, so maybe three 400w lights along each side would work better. In any case you'll need cooling air ducted from the lights that's ejected outside, in addition to the a/c unit. Done correctly, an air inlet in the floor can supply both the fresh air for the plants as well as the cooling air for the lights.

Done right, you trailer can be "teh killa" setup! A word of caution, though. With this setup you are already over 40 amps on a 110 feed, so be sure to have it properly wired. We're not talking about putting a single grow light in a spare bedroom here...