I am working on developing a very specific patent for the defense industry. My idea requires the use of a synthetic material only manufactured by one company. They will not sell the raw material to anyone in bulk, or in any other configuration than their finished product. How do I go about protecting my idea, but have them manufacture it?
You do not need any rights to the material to get a patent on a novel thing made with the material. Patents do not infringe patents, products infringe patents.
Presumably you understand the properties of the material so that you can show how it functions in your system. If the composition of the material is a trade secret you may have a hard time characterizing it your claims. Identifying a material by trademark name is rarely, if ever, allowed in a claim.
If other materials function, but just not as well, the patent does not need to revolve around the special material only.
If and when you get the patent, you can't make it because you can't get the material and they can't make it because you have the patent. If there is a large and lucrative market to be served, you and they should be able to work out a mutually agreeable deal.