The most important question is whether the county has an easement or owns the right of way. In most cases, the county requires a dedication of the road right of way before accepting it as a county road. If it is an easement, then one must look at the purpose of the easement. If it is for road and utility purposes, there is certainly a strong argument that pedestrian use along the side of the road in the remainder of the easement is an ancillary use to the "road" purpose of the easement, and the public can walk within the easement area. If it is road right of way, then the county owns it. Again, pedestrian use is an ancillary use of the public "road". If the county owns it, then it would be up to the county, not the adjacent landowner, to impose any limits on pedestrian use. It is common for q substantial open area to exist between the edge of the pavement and the edge of the right of way.
You should consult an attorney to obtain and review the documents creating the easement or right of way and advise you of your (and your children's) rights.
If the easement is for the benefit of the county and is limited to utilities and road improvements, you and your kids do not have the right to use it. You indicate, "I have my kids walk in the open 12' area of his property for safety reasons." The operative word there is, "his." If it is his property, you and your kids do not have a right to go on to it. You could be liable for trespassing if you do. Consider having your kids take an alternate route if you are legitimately concerned about safety. Alternatively, you could lobby the county or city that maintains the road to install sidewalks.
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I agree with the previous answers and you could look up the deed and easements with respect to the property to find out who really owns and who has easement rights in the area in question. People will frequently claim more than they have a right to on both sides.
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