+1 on a good fender; you can tow cover-up with a little more safety that way.
what i don't get is why parents don't use a long fender (i.e., fender+mud flap) on their bicycle's rear wheel when towing a child trailer at all times... it's not hard to see how much little (and big) junk gets flung 1-4ft. behind the bike. why the heck would you want to have a kid constantly exposed to that? a rear fender without the additional flap still leaves several inches of tire-spray angle (as tested when riding through autumn leaves last year)---though it's certainly better than nothing; a DIY mud flap i cooked up from a recycled plastic bottle kept the tire kick-back below 3in on the trialer---acceptable, given the trailer widow is at about 8-ish inches.
i personally leave my rear fender on all of the time, but even if i didn't, the 10 minutes it would take to install it before a ride seems worth it, given the nature of the cargo. moreover, even if you didn't have fender mounts, they make fenders for bikes without mounts that at least substantially mitigate the kick-back.