Big chains can be good for developing a well rounded base of knowledge, maybe it's not coffee knowledge as much as general business knowledge. Learn what you can from them, maintain a good attitude, and keep working toward your dream. You've got to do what makes you happy, but sometimes what makes you happy in the long run isn't much fun in the short term.
Bob's advice is good. Learn everything that you can while there.
Are you actively developing your shop concept right now? By actively developing I mean creating your detailed business plan, sketching up bar layout concepts, creating a visual design concept board (with color chips, fabric swatches, and pictures from catalogs and magazines), figuring out sizes, researching overhead expenses, figuring out target demographic and general locations, etc. If so, great! If not, you should start today. There's a difference between wanting to open a coffee shop and actively working to make it happen.
When we were developing our shop concept, I was working at a fairly well-run shop. It was so great to have that as a point of reference. Everything from "how many cups will we go through a week" to product percentage mix to menu pricing had a data point that was the next shift away.
There's a theory of small business structure that has you approach your operation as though it were the first store of a franchise. They suggest that you create processes and systems to handle everything. It is really a good approach, as it makes it possible for employees to run things just as well as you when you are not there. (Read "The E-Myth" for more on this). If you think about it, that's the one thing that large chains are really good at - making processes and systems so that anyone can do it.
Their suggestion is to make an operations manual. This manual details every process required to run your business - from brewing the coffee to cleaning checklists. Your current employer probably has one. You should have one too, though it may not need to be quite so formal. A spiral notebook with sketches, checklists, and concepts written in it is better than nothing.
My suggestion is to take a couple of questions to work with you every day, with the goal being to bring home the answers. You get to play secret agent for a little while, which can be fun. That doesn't mean make your cafe run exactly like your current employer, with every observation should come the question "how could this be done better". This gives your shifts more purpose, not that paying the bills isn't purpose enough.
On the question of jackass customers... use this as an opportunity to practice dealing with difficulty with a smile. Much as you'd like to think that you'll kick these people out for behaving badly when you own the joint, chances are that you won't. Well, you'll kick some out, but not as many as you'll want to.
Should you stay? I'd say stay until you've learned all that you can from them. I wouldn't leave until your business plan and operations manual were finished though.
I hear ya! I'm currently experiencing the exact same thing.
My previous place of employment was a local chain staffed by knowledgeable people that trained me very well. Maybe TOO well