You can record an easement without the consent of the servient estate on anything. Recording doesnt make it legal as the recording office does not validate matters of law, or verify property owners consent.
If the owner of the property at issue did not sign the easement grant it is void "ab initio" and therefore void as a matter of law. It was void at inception without the property owners signiture. Only the owner can grant easements, and outline the scope of the easement grant. And if subsequent owners "acquiesed" to the recorded grant, or relied upon the recorded grant, too bad, it only applies to them, not to you. Thats the law. At least in Missouri.
If it is their only access to their property you will have an impossible case. You can not block their ingress and win. Try to work out selling an easement for ingess/egress to them, legal fees at their expense, and try to make nice with your neighbors. Easements for ingress depend on length of easement area and extent of use but for just road purposes, a couple grand seems reasonable to avoid litigation (very expensive) and maintain a civil relaitionship with these folks. Good luck to you!