At a minimum, what the theater did was not a crime. When you are in a movie theater you have what is called a "license" from the theater to be present, which is revocable at will without due process (possibly subject to breach of contract damages) and not a property right to be in the theater the way that a tenant who must be evicted does.
As a practical matter, given that the amount in controversy is, at most, $25 or so, and this is not a situation where the prevailing party would get their attorneys' fees, this is not cost effective to litigate, regardless of who is correct, even in small claims court without an attorney.
Whether or not the theater breached its contract isn't perfectly clear, because usually, the contract between a movie goer and a movie theater is not spelled out in any writing provided to the movie goer, incorporated by reference in something disclosed to the movie goer, or signed by either of the parties, or even with an oral offer and acceptance setting forth all of the terms of the agreement. (Of course, if a written terms of service is actually provided to the movie goer, or a reference to where it can be found is provided to the movie goer, those terms will control and the contract will almost certainly be written to allow the movie theater to do what it did in this case.) In the frequent case where this is not done, the contract between a movie goer an a movie theater is usually a contract implied in fact whose terms at the edges aren't terribly well defined and there is little case law to tell us what the terms of the contract is, because the cases aren't worth litigating up to an appellate court where binding precedents are made.
Indeed, one reason that movie theaters may have declined to put their implied in fact contracts with movie goers in writing is to leave the situation ambiguous so as to discourage someone whose case would be clear even if for a small dollar amount, if the terms of the contact were clear, from suing them over issues like this one. When the stakes are small and the outcome is always uncertain, it almost never makes sense to sue.
There is certainly a colorable argument that you breached the contract by being present without an adult at an R-rating movie when the public statements about an R rating made available to the movie goers says that rated R means only admitted with a person over the age of 17, contrary to the theater's policies on that issue, although it isn't perfectly clear if this is a suggestion or a binding term of the agreement.
Another fair interpretation of the contract between a movie goer and the movie theater is that a movie goer can be removed from any movie whenever, if in the reasonable opinion of the movie theater management, good cause exists to do so, and that its discretion should be upheld so long as it acts in good faith and in a non-discriminatory manner.
I don't agree, however, that the question of whether or not you breached a contract was unambiguously clear, because the terms of the agreement are not well defined. I would give you at least a 20% chance of prevailing if you took the issue to court although I would agree that it is more likely than not that you would not prevail if you took the issue to court.