Will Cinnamon ever dissolve in a cocktail?
Cinnamon is the bark of a tree. It is either sold as rolled strips of bark (=cinnamon sticks) or ground. 

It will not dissolve, neither in water nor in alcohol. 

What you want to do is basically the same as was done commercially with the vanilla extract you are already using:  Extract the taste, then discard the bark itself.


Alcohol is a good choice for extracting volatile aromatics. You could try and soak a few cinnamon sticks or a few tablespoons of ground cinnamon in a "neutral" alcohol like vodka or - if you are using it exclusively for your signature drink - use the brandy. This process might take from a few days to a few weeks, so nothing you can do "on the spur of the moment". 
Another good carrier for the cinnamon taste would be water. You can simmer a few cinnamon sticks in water, then sieve. This is the same method that is used for mulled wine or mulled cider. To extend the shelf life of the "cinnamon water", you might considering turning it into simple syrup by boiling it with an equal amount of sugar.


Whether you use water or alcohol is a question of personal taste and planned other uses. The shelf life of an alcohol based extract might be longer, but with a sufficiently high sugar content, clean handling and refrigeration the syrup will last long, too. Time is a factor: The syrup can be ready and cooled in an hour or so, whereas the alcohol will take significantly more time.

Both methods work for vanilla, too - you could even make a "instant mix" for your drink.

Be warned, though: Filtering ground cinnamon from a liquid can be quite a hassle. It tends to clog coffe filters, but is too fine to be held back by a sieve. If you decide to use ground cinnamon because that's what you have at hand, consider letting it settle at the bottom of your container and carefully decanting the liquid from top. A coffe filter or a cloth-lined sieve can catch stray particles. You should get much better results by using whole or coarsely crushed cinnamon sticks.



There has been an ongoing discussion on what kind of cinnamon to use, so a short wrap-up here:

Cinnamon is derived from a group of plants, which vary in their properties and compounds. Especially coumarin, a substance also found in tonka bean, woodruff and other plants, has been widely discussed for its toxicity and is regulated in the EU. 


Cassia cinnamon has the highest content whereas 
true / Ceylon / Sri Lanka cinnamon contains only traces.


From a culinary point, the cheaper cassia, which contains more bark and is usually sold ground or in pieces, is often considered inferior in taste to the true cinnamon, which often comes in sticks. 

I will not venture a statement here, neither on health nor culinary claims. 
I am sure every reader of this post is capable of making an informed decision.