It's time to go to corporate headquarters. But don't call them. Send them your complaint in writing and request a written reply within 10 business days. Why? Because you are now at the point where you need to carefully document your interactions with them. If you talk to them in person or on the phone and there is a later dispute about who said what, it will be their word against yours. In a case of discrimination like this, if it comes down to your word against theirs your case will be dropped (it's your burden to prove discrimination occurred).
Send them a copy of this document:
And suggest they consult the U.S. Department of Justice's toll-free ADA information line (800 - 514 - 0301) to learn about their rights and obligations under federal laws that protect the disabled, such as the Americans with Disabilities Act.
If you do not receive a reply within 15 business days, send your letter again, but this time send it certified, return receipt requested. That will prevent them from claiming they never received your letter, and put them on notice you are serious.
If it still isn't resolved, go to your state's human rights commission. You could complain to the U.S. Department of Justice, but it takes about three times as long to get a case through them as it does to get the case handled at the state level. The DOJ is also very selective about which cases they take on and won't take on yours unless they see a pattern of discrimination (receive complaints from several different people each having a similar experience).
You can find information about contacting your state's human rights commission, attorney general, and a bunch of info on various state laws at Service Dog Central's collection of service dog law information:
Throughout the process it is essential that you maintain your cool. Be very polite. Remember that anything you write, say or do could be examined by a judge if this complaint goes to court. You'll want to show by your behavior that you were being reasonable and they were being unreasonable.
You always have the option to pursue it privately in civil court, but the last time I got an estimate on a case I was quoted $7,000 up front in attorney's fees. If you go through a government enforcement agency, such as your state's human rights commission or the U.S. Department of Justice, that agency will pick up the costs of taking it to court instead of you.