Starting from the park, ride as far you like with children with no worry of traffic. Remember that the last quarter of a mile will be a climb as you head back to the parking lot so don't over do it.
This road is paved between Hwy 70 and Rico Road but it is unlikely you'll see any cars. Once east of Rico Road, you'll pass through a gate that indicates you are headed for Cochran Mill Park. The gate keeps all traffic off this road except during deer season or when logging operations are taking place.
The road surface is nearly a trail and changes difficulty after each rain and depending on how long it has been since loggers smoothed it out. This road gets an intermediate difficulty rating as it can be difficult for cross bikes.
Cross bikes might want to ride the Dirty Sheets Gravel Loop in reverse so that difficult sections are done as climbs and not as descents. Some sections of the road can become iced over on the coldest winter days. The city has scheduled and budgeted the ditches and culverts to be cleaned in the fall of 2016 so this should help greatly.
This is great option for beginner riders that aren't ready to tackle the trails in Cochran Mill Park yet.