Really that's too esoteric for most anonymous mostly amateurs on the internet. You probably should find a qualified tax advisor.
So here's the problem(s).
Regarding deductible medical expenses. A service animal (as defined by the ADA) is an animal that is trained to perform one or more assistive tasks. Service animal costs are deductible medical expenses. A comfort or support animal, that provides support through it's natural behaviors, is not a service animal and is not protected under the ADA (does not have to be accommodated by airlines, employers, etc although many do anyway). It is not clear that comfort animal costs are deductible medical expenses. It is at the very least, a higher bar to prove that the animal is part of medical treatment to alleviate a medical condition and not a personal expense. See this especially the followups at the bottom. http://doglawreporter.blogspot.com/2010/07/irs-affirms-deductibility-of.html
Here is part of the IRS ruling,
“In determining allowability, many factors must be considered. Consideration should be accorded the motive or purpose of the taxpayer, but such factor is not alone determinative. To accord it conclusive weight would make nugatory the prohibition against allowing personal, living, or family expenses. Thus also it is important to inquire as to the origin of the expense. Was it incurred at the direction or suggestion of a physician; did the treatment bear directly on the physical condition in question; did the treatment bear such a direct or proximate therapeutic relation to the bodily condition as to justify a reasonable belief the same would be efficacious; was the treatment so proximate in the time to the onset or recurrence of the disease or condition as to make one the true occasion of the other, thus eliminating expense incurred for general, as contrasted with some specific, physical improvement?”
That's not directly to your question because you are not providing medical care, but it should illuminate the IRS thinking on the matter.
The other issue is that deductible business expenses are those that are ordinary and neccessary. The IRS says this,
To be deductible, a business expense must be both ordinary and necessary. An ordinary expense is one that is common and accepted in your trade or business. A necessary expense is one that is helpful and appropriate for your trade or business. An expense does not have to be indispensable to be considered necessary.
And the IRS is always concerned about people who improperly characterize non-deductible personal expenses as business expenses in order to obtain a deduction.
So the factors that will inform this deduction will start with, it is an ordinary and necessary practice of being a marital therapist to have a dog around to help the clients relax. Is this your idea, or has this been coming along in the practice (you found out about in CPE, journals, etc.) To what extent does the animal become a meaningful part of your practice? Will it really be on site every day, or only when clients request, or does the dog end up staying at home. It's your dog you already own, so motive will come into play. Is the training specific to the needs of your job, or is it a more generic type of obedience training.
Having said that, I think that food and treats consumed at work could possibly be a business expense, along with toys, dog bed, cage or travel carrier. Sufficiently specialized training could be deductible. Food at home would not be deductible. Routine or emergency vet care would probably not be deductible on the grounds that the animal would require the same care whether it was involved in the business or not. (Unlike a service animal where vet care is provided because the purpose of the animal is to provide defined types of assistance to a person with defined medical needs.)
Hope this helps. Interesting question.
