Welcome to SR kkm. You will find a LOT of support here.
Since your dog is a service dog, you are protected under the American with Disability Act and you cannot be turned down for housing or employment.
This is a service animal and as such a "tool" (kind of like a cane or a wheelchair) to help you function. Under the law, it is not a pet or your baby, it is a protected instrument.
Here is a link to the ADA website which will answer your questions.
https://www.ada.gov/regs2010/service_animal_qa.html
Also
Under the Americans with Disabilities Act (ADA), privately owned businesses that serve the public, such as restaurants, hotels, retail stores, taxicabs, theaters, concert halls, and sports facilities, are prohibited from discriminating against individuals with disabilities. The ADA requires these businesses to allow people with disabilities to bring their service animals onto business premises in whatever areas customers are generally allowed.
A sober house would be such an establishment. They do have to provide reasonable accommodation under federal law.
You might want to look up the Oxford Houses and see if they have a chapter in Costa Mesa
http://www.oxfordhouse.org/userfiles/file/
I work for a non profit and one of our shelters made the mistake a few years back to turn down someone with a service animal, the person filed a complain with the Office Of Civil Rights and we were mandated to take classes about the ADA and also take Sensitivity Training.