The title deeds - more specifically the mapping on the title document(s) - are not always conclusive evidence of ownership and that is one of the problems with this type of situation.
I would endorse Jumpstartdublin's point about written confirmation of right of way. For example, we have a shared drive at the side of the house. It is shared with the adjacent property only. The two properties respective title deeds contain permanent undertakings that each property must give the other right of passage over it by vehicle or on a horse ! I would look for any such provision in your deeds.
Additionally, I would seek written confirmation from DCC on their position in relation to ownership of the driveway. Specifically, I would be exploring the proposition that the lane is effectively the same as a public road.
I cannot see how the insurers can refuse to cover the risk if the lane can be likened to a public road.
BTW the concept of ownership in relation to land can be a bit fluid. If you have used the land as if you owned it you could have effective title to it by adverse possession for 20 years plus (not always an advantage !). Equally, if neighbours have been exercising right of passage over it for a similar term of years they may acquire an easement or right to traverse it.