This answer has two parts:
1. Create your Fields. If you have CBSubs installed, you can select the following configuration from the Field CBSubs preferences on the right side of the Field edit screen:
A. Yes, CBsubs controls detailed field access
A.1 For others viewers: Select the plan(s) that CAN see the field
A.2 No, profile owner himself is also restricted: Select the plans(s) that CAN see the field
A.3 Both Options, No, moderators are also restricted
The above options will allow only the users with the plan you have created see the field in their own profile.
2. Create the Plan. Under the workflows tab, select the fields you DO NOT want that plan to see at registration. For your regular user plan, this would be all of the dealer fields. For your dealer plan, you would likely show all of the fields.
Good luck.