My employer canceled on me (I am a contract worker) and didn't pay the termination fee we discussed. I want to show him the actual law so that he may understand that he should pay me because I have a legal right. The fee was written in the actual contract.
It isn't ordinarily written in law. The only law directly pointing this out would likely be if you can show a court case with similar facts where an employer was made to pay.
Parties have obligations under contracts, which in most cases are established by the contract itself rather than the law. Those obligations are enforced by bringing a lawsuit in court for "breach of contract." (Or, if the contract specifies, going to arbitration).
If a party refuses to honor their contract, the typical next step is to have a lawyer to write the party a sternly worded "demand letter" on law firm letterhead that makes the party realize he, she, or it has a legal obligation and it will be cheaper to pay than to fight.
Contract law is common law, not statute law, that is, there is no piece of legislation that you can point to and say "there's the law".
What you need to do is find cases, preferably decided in your state that support the enforcement of such a clause and quote the cases to the principal.