We rode with our kids at that age, but never over about 10 miles. Our Chariot trailer attaches to the axle, leaving the rack attach points open. Some of the cheap trailers clamp to the tubing, and may interfere (or may not).
With that short of rides, we merely put supplies in the back of the trailer.
That looks like a fun bike. My one concern is not having low enough gearing with the single speed. When pulling a trailer I'm usually in a gear or two lower than what I would be without the trailer, and perhaps 3-4 going up a big hill. If this is a problem, perhaps you can find a bike shop to swap out the front gear for a smaller one?
Enjoy your rides with your kids. They grow up fast, and only so much time to make great memories on summer outings.