What contract book? In general, company employee handbooks are simply statements of company policies and do not make enforceable contracts. If they are simply statements of policy then management may choose to ignore them if they wish; no law requires they follow their own policy (though of course good managment would do that or they'd not have bothered coming up with the policy manual in the first place). If you are referring to the collective bargaining agreement (CBA) your union has with the employer, then it is the union rep (usually the shop steward) that needs to make this an issue with management. You indicate that there is no stated parking policy in whatever document you are looking at, and if there isn't anything in the CBA about it, all your union rep can do is raise a fuss about it and hope that management doesn't want to deal with that and will agree to something that will satisfy most everyone. If management is unwilling to discuss the issue now, then it'll have to wait until it's time to renegotiate the CBA.
The bottom line is that management runs the company, and unless what management does either violates the law or the CBA it may do as it pleases and set the policies it wants. So if the employees want this change, the better approach may be one of persuasion rather than confrontation.