Let me first answer this with what SHOULD happen. Your subsupplier has described a process to make a part that they sell to you. I am going to assume it is a correct and to standard PPAP submission. You should then be signing a Part Submission Warrant provided by the subsupplier that basically says "We, your customer, agree with this process to make and control the quality of your product."
You are then going to take this component and include it in some process of yours, that is going to make a product for YOUR customer. You should submit a PPAP describing YOUR process (with the PFD,
PFMEA, Control Plan and all the other stuff) to YOUR customer. And you should include the warrant(s) you signed for your suppliers. Which let your customer know that you have checked what your supplier has done. And that SHOULD be enough.
Now lets talk about what MAY happen. Your customer may not trust you. Probably won't. And they will want to review the processes that are generating some of the key components. Especially if there is a lot of metallurgy involved and you are passing them through. Why don't they trust you? THAT's another discussion, but .... the key points for you are.
1) Your customer has requested a control plan or other key information from your supplier.
2) From a business standpoint, you MUST ask the supplier's permission to forward it. I am reasonably sure there is some NDA running around, AND it's just good manners.
3) If your supplier says "Nope. Not forwarding MY stuff to YOUR customer." Then you politely tell your customer that your supplier considers the material proprietary and he can come review it with you at YOUR location or the sub suppliers location, but you cannot forward it. (Happens all the time).
4) If your supplier say "I'm good." Then forward it and make your customer happy. If your customer is being a pain and you want to needle him a bit, you COULD open with "Would you like to sign my sub suppliers warrant?" Which he will answer "No." Then you can ask "Why, then, do you need to see his submission?"
All of us in "quality" should be data and procedure driven individuals. I am always amazed at the amount of politics involved.